Best Known (44−22, 44, s)-Nets in Base 25
(44−22, 44, 153)-Net over F25 — Constructive and digital
Digital (22, 44, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (10, 32, 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
- digital (1, 12, 27)-net over F25, using
(44−22, 44, 342)-Net over F25 — Digital
Digital (22, 44, 342)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2544, 342, F25, 22) (dual of [342, 298, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2544, 624, F25, 22) (dual of [624, 580, 23]-code), using
(44−22, 44, 79897)-Net in Base 25 — Upper bound on s
There is no (22, 44, 79898)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 32 313892 643429 020868 083846 106653 893200 955091 646460 006518 034193 > 2544 [i]