Best Known (26, 53, s)-Nets in Base 25
(26, 53, 200)-Net over F25 — Constructive and digital
Digital (26, 53, 200)-net over F25, using
- t-expansion [i] based on digital (25, 53, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(26, 53, 332)-Net over F25 — Digital
Digital (26, 53, 332)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2553, 332, F25, 27) (dual of [332, 279, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2553, 624, F25, 27) (dual of [624, 571, 28]-code), using
(26, 53, 92241)-Net in Base 25 — Upper bound on s
There is no (26, 53, 92242)-net in base 25, because
- 1 times m-reduction [i] would yield (26, 52, 92242)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4 931050 372615 172193 711390 810460 061892 826869 020146 123581 620715 087072 906865 > 2552 [i]