Best Known (67−54, 67, s)-Nets in Base 25
(67−54, 67, 126)-Net over F25 — Constructive and digital
Digital (13, 67, 126)-net over F25, using
- t-expansion [i] based on digital (10, 67, 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
(67−54, 67, 1326)-Net in Base 25 — Upper bound on s
There is no (13, 67, 1327)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 4678 366971 175671 977284 277768 229190 757919 371635 486621 997321 801671 705425 250704 676967 277626 008825 > 2567 [i]