Best Known (40−33, 40, s)-Nets in Base 49
(40−33, 40, 57)-Net over F49 — Constructive and digital
Digital (7, 40, 57)-net over F49, using
- net from sequence [i] based on digital (7, 56)-sequence over F49, using
(40−33, 40, 92)-Net over F49 — Digital
Digital (7, 40, 92)-net over F49, using
- t-expansion [i] based on digital (3, 40, 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
(40−33, 40, 1859)-Net in Base 49 — Upper bound on s
There is no (7, 40, 1860)-net in base 49, because
- 1 times m-reduction [i] would yield (7, 39, 1860)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 832959 559971 812405 705370 790742 103488 012855 909297 861807 624967 355393 > 4939 [i]