Best Known (67−55, 67, s)-Nets in Base 25
(67−55, 67, 126)-Net over F25 — Constructive and digital
Digital (12, 67, 126)-net over F25, using
- t-expansion [i] based on digital (10, 67, 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
(67−55, 67, 1175)-Net in Base 25 — Upper bound on s
There is no (12, 67, 1176)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 66, 1176)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 185 927672 208285 655939 053276 289683 283375 694441 998701 631619 008828 793954 519484 340767 654484 377025 > 2566 [i]