Best Known (3, 3+∞, s)-Nets in Base 25
(3, 3+∞, 52)-Net over F25 — Constructive and digital
Digital (3, m, 52)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(3, 3+∞, 56)-Net over F25 — Digital
Digital (3, m, 56)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(3, 3+∞, 95)-Net in Base 25 — Upper bound on s
There is no (3, m, 96)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (3, 90, 96)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(2590, 96, S25, 87), but
- the linear programming bound shows that M ≥ 13 668865 221078 739256 015071 809629 879850 936124 576679 322503 501034 318504 064092 312472 780759 593604 486823 448240 784273 366443 812847 137451 171875 / 20 559539 > 2590 [i]
- extracting embedded orthogonal array [i] would yield OA(2590, 96, S25, 87), but