Best Known (21, 21+24, s)-Nets in Base 49
(21, 21+24, 344)-Net over F49 — Constructive and digital
Digital (21, 45, 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
(21, 21+24, 443)-Net over F49 — Digital
Digital (21, 45, 443)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4945, 443, F49, 24) (dual of [443, 398, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4945, 480, F49, 24) (dual of [480, 435, 25]-code), using
(21, 21+24, 240073)-Net in Base 49 — Upper bound on s
There is no (21, 45, 240074)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 11450 494589 723825 626029 524582 602660 807510 113176 266953 439732 677515 202509 956225 > 4945 [i]