Best Known (83−69, 83, s)-Nets in Base 25
(83−69, 83, 126)-Net over F25 — Constructive and digital
Digital (14, 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
(83−69, 83, 130)-Net over F25 — Digital
Digital (14, 83, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(83−69, 83, 1308)-Net in Base 25 — Upper bound on s
There is no (14, 83, 1309)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 82, 1309)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4 296309 950594 965451 773248 728649 590410 039799 510427 847359 949404 691170 752188 221167 080038 681547 047058 800173 229427 704625 > 2582 [i]