Best Known (24, 51, s)-Nets in Base 49
(24, 51, 344)-Net over F49 — Constructive and digital
Digital (24, 51, 344)-net over F49, using
- t-expansion [i] based on digital (21, 51, 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
(24, 51, 498)-Net over F49 — Digital
Digital (24, 51, 498)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4951, 498, F49, 27) (dual of [498, 447, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4951, 600, F49, 27) (dual of [600, 549, 28]-code), using
(24, 51, 374034)-Net in Base 49 — Upper bound on s
There is no (24, 51, 374035)-net in base 49, because
- 1 times m-reduction [i] would yield (24, 50, 374035)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 3 234518 053628 963917 856616 209372 495207 562474 873699 499627 906710 612743 008036 199506 092625 > 4950 [i]