Best Known (39−31, 39, s)-Nets in Base 49
(39−31, 39, 58)-Net over F49 — Constructive and digital
Digital (8, 39, 58)-net over F49, using
- net from sequence [i] based on digital (8, 57)-sequence over F49, using
(39−31, 39, 92)-Net over F49 — Digital
Digital (8, 39, 92)-net over F49, using
- t-expansion [i] based on digital (3, 39, 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
(39−31, 39, 2553)-Net in Base 49 — Upper bound on s
There is no (8, 39, 2554)-net in base 49, because
- 1 times m-reduction [i] would yield (8, 38, 2554)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 16945 172835 782684 544419 660639 610394 270674 074753 925148 689689 161249 > 4938 [i]