Best Known (40, 85, s)-Nets in Base 5
(40, 85, 78)-Net over F5 — Constructive and digital
Digital (40, 85, 78)-net over F5, using
- t-expansion [i] based on digital (38, 85, 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
(40, 85, 1039)-Net in Base 5 — Upper bound on s
There is no (40, 85, 1040)-net in base 5, because
- 1 times m-reduction [i] would yield (40, 84, 1040)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 51805 296836 704135 829417 588513 457223 395145 854869 930581 347585 > 584 [i]