Best Known (21, 21+23, s)-Nets in Base 49
(21, 21+23, 344)-Net over F49 — Constructive and digital
Digital (21, 44, 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+23, 513)-Net over F49 — Digital
Digital (21, 44, 513)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4944, 513, F49, 23) (dual of [513, 469, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4944, 800, F49, 23) (dual of [800, 756, 24]-code), using
(21, 21+23, 413902)-Net in Base 49 — Upper bound on s
There is no (21, 44, 413903)-net in base 49, because
- 1 times m-reduction [i] would yield (21, 43, 413903)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 4 769167 365950 247802 719272 682316 237084 678280 162504 484194 430776 980602 131185 > 4943 [i]