Best Known (22, 22+24, s)-Nets in Base 49
(22, 22+24, 344)-Net over F49 — Constructive and digital
Digital (22, 46, 344)-net over F49, using
- t-expansion [i] based on digital (21, 46, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(22, 22+24, 531)-Net over F49 — Digital
Digital (22, 46, 531)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4946, 531, F49, 24) (dual of [531, 485, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, 800, F49, 24) (dual of [800, 754, 25]-code), using
(22, 22+24, 332045)-Net in Base 49 — Upper bound on s
There is no (22, 46, 332046)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 561083 070784 517493 679040 925404 350992 727460 603905 790509 118945 759141 641817 358721 > 4946 [i]