Best Known (10, 22, s)-Nets in Base 25
(10, 22, 126)-Net over F25 — Constructive and digital
Digital (10, 22, 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
(10, 22, 159)-Net over F25 — Digital
Digital (10, 22, 159)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2522, 159, F25, 12) (dual of [159, 137, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2522, 208, F25, 12) (dual of [208, 186, 13]-code), using
(10, 22, 16661)-Net in Base 25 — Upper bound on s
There is no (10, 22, 16662)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 5 684964 424842 006473 888756 234017 > 2522 [i]