Best Known (69−59, 69, s)-Nets in Base 25
(69−59, 69, 126)-Net over F25 — Constructive and digital
Digital (10, 69, 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
(69−59, 69, 907)-Net in Base 25 — Upper bound on s
There is no (10, 69, 908)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 68, 908)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 118169 121965 908827 469681 991146 867732 027789 928060 183254 183720 682189 861378 394702 160648 487387 036065 > 2568 [i]