Best Known (98−80, 98, s)-Nets in Base 25
(98−80, 98, 126)-Net over F25 — Constructive and digital
Digital (18, 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
(98−80, 98, 153)-Net over F25 — Digital
Digital (18, 98, 153)-net over F25, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(98−80, 98, 1726)-Net in Base 25 — Upper bound on s
There is no (18, 98, 1727)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 99896 048943 121615 882714 456927 473592 145858 956807 616720 243528 588562 174479 520060 487340 839141 780070 976181 859770 670002 683672 253709 046212 602945 > 2598 [i]