Best Known (31−29, 31, s)-Nets in Base 49
(31−29, 31, 52)-Net over F49 — Constructive and digital
Digital (2, 31, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
(31−29, 31, 78)-Net over F49 — Digital
Digital (2, 31, 78)-net over F49, using
- net from sequence [i] based on digital (2, 77)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 2 and N(F) ≥ 78, using
(31−29, 31, 488)-Net in Base 49 — Upper bound on s
There is no (2, 31, 489)-net in base 49, because
- 9 times m-reduction [i] would yield (2, 22, 489)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 15 390880 362184 448267 702889 490736 305633 > 4922 [i]