Best Known (51−30, 51, s)-Nets in Base 49
(51−30, 51, 344)-Net over F49 — Constructive and digital
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
(51−30, 51, 74670)-Net in Base 49 — Upper bound on s
There is no (21, 51, 74671)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 158 502592 872880 017624 498041 117549 013363 419495 456239 708052 176052 640264 813497 255685 522481 > 4951 [i]