Best Known (98−82, 98, s)-Nets in Base 25
(98−82, 98, 126)-Net over F25 — Constructive and digital
Digital (16, 98, 126)-net over F25, using
- t-expansion [i] based on digital (10, 98, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(98−82, 98, 150)-Net over F25 — Digital
Digital (16, 98, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(98−82, 98, 1454)-Net in Base 25 — Upper bound on s
There is no (16, 98, 1455)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 101031 365249 896461 771352 215657 094048 669040 748649 856998 454785 100763 939521 719161 309049 855398 286843 804666 398490 869927 685068 895844 439285 129385 > 2598 [i]