Best Known (13, 13+71, s)-Nets in Base 25
(13, 13+71, 126)-Net over F25 — Constructive and digital
Digital (13, 84, 126)-net over F25, using
- t-expansion [i] based on digital (10, 84, 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
(13, 13+71, 1178)-Net in Base 25 — Upper bound on s
There is no (13, 84, 1179)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 83, 1179)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 107 513603 225578 166998 808644 643455 409349 841426 044320 489232 112268 708403 880634 440306 228608 605605 365476 573199 796862 791705 > 2583 [i]