Best Known (3, 3+61, s)-Nets in Base 25
(3, 3+61, 52)-Net over F25 — Constructive and digital
Digital (3, 64, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+61, 56)-Net over F25 — Digital
Digital (3, 64, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+61, 234)-Net in Base 25 — Upper bound on s
There is no (3, 64, 235)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2564, 235, S25, 61), but
- the linear programming bound shows that M ≥ 406265 266299 137864 987288 210253 538383 699575 775084 136679 357077 797440 804859 362140 089018 566868 617199 361324 310302 734375 / 1 368430 194079 349929 119791 > 2564 [i]