Best Known (12, 12+49, s)-Nets in Base 25
(12, 12+49, 126)-Net over F25 — Constructive and digital
Digital (12, 61, 126)-net over F25, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(12, 12+49, 1263)-Net in Base 25 — Upper bound on s
There is no (12, 61, 1264)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 60, 1264)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 752721 593803 438679 550068 150705 766676 011359 212357 401216 501520 213209 133632 992950 170625 > 2560 [i]