Use R to Randomly Assign of Participants to Treatments on a Daily Basis

The Problem:

I am attempting to use R to generate a random study design where half of the participants are randomly assigned to "Treatement 1" and the other half are assigned to "Treatment 2". However, because half of the subjects are male and half are female and I also want to ensure that an equal number of males and females are exposed to each treatment, half of the males and females should be assigned to "Treatment 1" and the remaining half should be assigned to "Treatment 2".

There are two complications to this design: (1) This is a yearlong study and the assignment of participants to treatment must occur on a daily basis; and (2) Each participant must be exposed to "Treatment 1" a minimum 10 times in a 28 day period.

Is this even possible to automate this in the R interface? I assume so, but I think my beginner status as an R programmer prohibits me from finding the solution on my own. I have been struggling for days to figure out how to actualize this, and have looked through many similar-sounding posts on this site that were not able to be successfully applied here. I am hoping someone out there knows some tricks that could help me get unstuck in solving this problem, any advice would be greatly appreciated!

What I Have Tried:

Specific Information

# There are 16 participants
p <- c("P01", "P02", "P03", "P04", "P05", "P06", "P07", "P08", "P09", "P10", "P11", "P12", "P13", "P14", "P15", "P16")

# Half are male and half are female
g <- c(rep("M", 8), rep("F", 8))

# I make a dataframe but this may not be necessary
df <- cbind.data.frame(p,g)

# There are 365 days in one year
d <- seq(1,365,1)

...unfortunately, I am not sure how to proceed from here.

Ideal Outcome:

I am envisioning something approximate to this table as the outcome:

Basically there is a column for each participant and a row for each day. Associated with each day is an assignment to either Treatment 1 (T1) or Treatment 2 (T2), with 4 of the 8 males and 4 of the 8 females being assigned to T1 and the remainder to T2. These treatments are reassigned every day for 1 year. Not depicted in this chart is the need for each participant to be exposed to T1 at least 10 times in a 28-day period. The table does not have to look like that if something else makes more sense!