Best Known (55−41, 55, s)-Nets in Base 25
(55−41, 55, 126)-Net over F25 — Constructive and digital
Digital (14, 55, 126)-net over F25, using
- t-expansion [i] based on digital (10, 55, 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
(55−41, 55, 130)-Net over F25 — Digital
Digital (14, 55, 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
(55−41, 55, 2048)-Net in Base 25 — Upper bound on s
There is no (14, 55, 2049)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 54, 2049)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 3108 725061 668859 096257 895158 022737 121853 271551 689691 382366 528389 340051 207521 > 2554 [i]