Best Known (39, 39+37, s)-Nets in Base 5
(39, 39+37, 78)-Net over F5 — Constructive and digital
Digital (39, 76, 78)-net over F5, using
- t-expansion [i] based on digital (38, 76, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(39, 39+37, 92)-Net over F5 — Digital
Digital (39, 76, 92)-net over F5, using
(39, 39+37, 1530)-Net in Base 5 — Upper bound on s
There is no (39, 76, 1531)-net in base 5, because
- 1 times m-reduction [i] would yield (39, 75, 1531)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 26680 258537 282042 157956 488702 692702 813107 004209 351225 > 575 [i]