Best Known (6, 6+9, s)-Nets in Base 25
(6, 6+9, 66)-Net over F25 — Constructive and digital
Digital (6, 15, 66)-net over F25, using
- t-expansion [i] based on digital (4, 15, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
(6, 6+9, 86)-Net over F25 — Digital
Digital (6, 15, 86)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2515, 86, F25, 9) (dual of [86, 71, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2515, 104, F25, 9) (dual of [104, 89, 10]-code), using
(6, 6+9, 7203)-Net in Base 25 — Upper bound on s
There is no (6, 15, 7204)-net in base 25, because
- 1 times m-reduction [i] would yield (6, 14, 7204)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 37 267509 158063 389825 > 2514 [i]