Best Known (85−73, 85, s)-Nets in Base 25
(85−73, 85, 126)-Net over F25 — Constructive and digital
Digital (12, 85, 126)-net over F25, using
- t-expansion [i] based on digital (10, 85, 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
(85−73, 85, 1068)-Net in Base 25 — Upper bound on s
There is no (12, 85, 1069)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 84, 1069)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2720 444492 766548 493704 173635 214262 912612 039156 531389 214639 248017 241023 579496 547205 240919 404815 685376 086898 670367 369313 > 2584 [i]