Best Known (88−84, 88, s)-Nets in Base 25
(88−84, 88, 66)-Net over F25 — Constructive and digital
Digital (4, 88, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
(88−84, 88, 262)-Net in Base 25 — Upper bound on s
There is no (4, 88, 263)-net in base 25, because
- 2 times m-reduction [i] would yield (4, 86, 263)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(2586, 263, S25, 82), but
- the linear programming bound shows that M ≥ 124838 157887 948575 069973 603564 217894 140049 811879 259470 500094 671199 192064 814369 803279 087877 393316 825789 390511 262347 445431 419856 731736 217625 439167 022705 078125 / 73787 952480 415645 668068 103685 901541 > 2586 [i]
- extracting embedded orthogonal array [i] would yield OA(2586, 263, S25, 82), but