Best Known (11, 11+14, s)-Nets in Base 49
(11, 11+14, 150)-Net over F49 — Constructive and digital
Digital (11, 25, 150)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 4, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (0, 7, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 14, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 4, 50)-net over F49, using
(11, 11+14, 260)-Net over F49 — Digital
Digital (11, 25, 260)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4925, 260, F49, 14) (dual of [260, 235, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 300, F49, 14) (dual of [300, 275, 15]-code), using
(11, 11+14, 76572)-Net in Base 49 — Upper bound on s
There is no (11, 25, 76573)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 1 798509 151497 151664 766782 246346 492269 440273 > 4925 [i]