Best Known (22, 22+25, s)-Nets in Base 49
(22, 22+25, 344)-Net over F49 — Constructive and digital
Digital (22, 47, 344)-net over F49, using
- t-expansion [i] based on digital (21, 47, 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+25, 462)-Net over F49 — Digital
Digital (22, 47, 462)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4947, 462, F49, 25) (dual of [462, 415, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4947, 481, F49, 25) (dual of [481, 434, 26]-code), using
- an extension Ce(24) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(4947, 481, F49, 25) (dual of [481, 434, 26]-code), using
(22, 22+25, 332045)-Net in Base 49 — Upper bound on s
There is no (22, 47, 332046)-net in base 49, because
- 1 times m-reduction [i] would yield (22, 46, 332046)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 561083 070784 517493 679040 925404 350992 727460 603905 790509 118945 759141 641817 358721 > 4946 [i]