Best Known (61−51, 61, s)-Nets in Base 25
(61−51, 61, 126)-Net over F25 — Constructive and digital
Digital (10, 61, 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
(61−51, 61, 947)-Net in Base 25 — Upper bound on s
There is no (10, 61, 948)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 60, 948)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 763366 969795 646464 458951 010973 314113 348150 754222 458614 069663 549397 942538 303153 132513 > 2560 [i]