Best Known (2, 2+10, s)-Nets in Base 25
(2, 2+10, 28)-Net over F25 — Constructive and digital
Digital (2, 12, 28)-net over F25, using
- net from sequence [i] based on digital (2, 27)-sequence over F25, using
(2, 2+10, 46)-Net over F25 — Digital
Digital (2, 12, 46)-net over F25, using
- net from sequence [i] based on digital (2, 45)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 2 and N(F) ≥ 46, using
(2, 2+10, 243)-Net in Base 25 — Upper bound on s
There is no (2, 12, 244)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 60025 723085 725537 > 2512 [i]
- extracting embedded orthogonal array [i] would yield OA(2512, 244, S25, 10), but
- the linear programming bound shows that M ≥ 5 197276 439112 292423 248291 015625 / 86 772815 851171 > 2512 [i]