Best Known (83−68, 83, s)-Nets in Base 25
(83−68, 83, 126)-Net over F25 — Constructive and digital
Digital (15, 83, 126)-net over F25, using
- t-expansion [i] based on digital (10, 83, 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
(83−68, 83, 140)-Net over F25 — Digital
Digital (15, 83, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(83−68, 83, 1440)-Net in Base 25 — Upper bound on s
There is no (15, 83, 1441)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 108 032055 213807 573627 931025 971259 803848 499875 912735 597537 893870 966170 795934 322745 322099 843842 150202 429557 507494 140785 > 2583 [i]