Best Known (53−37, 53, s)-Nets in Base 49
(53−37, 53, 66)-Net over F49 — Constructive and digital
Digital (16, 53, 66)-net over F49, using
- net from sequence [i] based on digital (16, 65)-sequence over F49, using
(53−37, 53, 92)-Net over F49 — Digital
Digital (16, 53, 92)-net over F49, using
- t-expansion [i] based on digital (3, 53, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(53−37, 53, 12004)-Net in Base 49 — Upper bound on s
There is no (16, 53, 12005)-net in base 49, because
- 1 times m-reduction [i] would yield (16, 52, 12005)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 7767 769120 763316 709697 299591 252437 134291 755092 229931 100400 096552 648512 349422 096979 051489 > 4952 [i]