Best Known (42−21, 42, s)-Nets in Base 25
(42−21, 42, 153)-Net over F25 — Constructive and digital
Digital (21, 42, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (10, 31, 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, 11, 27)-net over F25, using
(42−21, 42, 335)-Net over F25 — Digital
Digital (21, 42, 335)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2542, 335, F25, 21) (dual of [335, 293, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 624, F25, 21) (dual of [624, 582, 22]-code), using
(42−21, 42, 101694)-Net in Base 25 — Upper bound on s
There is no (21, 42, 101695)-net in base 25, because
- 1 times m-reduction [i] would yield (21, 41, 101695)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2068 022941 586563 032324 460770 228512 296495 733865 917749 895953 > 2541 [i]