Best Known (1, 1+23, s)-Nets in Base 25
(1, 1+23, 27)-Net over F25 — Constructive and digital
Digital (1, 24, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
(1, 1+23, 36)-Net over F25 — Digital
Digital (1, 24, 36)-net over F25, using
- net from sequence [i] based on digital (1, 35)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 1 and N(F) ≥ 36, using
(1, 1+23, 113)-Net over F25 — Upper bound on s (digital)
There is no digital (1, 24, 114)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(2524, 114, F25, 23) (dual of [114, 90, 24]-code), but
- construction Y1 [i] would yield
- linear OA(2523, 27, F25, 23) (dual of [27, 4, 24]-code or 27-arc in PG(22,25)), but
- OA(2590, 114, S25, 87), but
- discarding factors 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]
- discarding factors would yield OA(2590, 96, S25, 87), but
- construction Y1 [i] would yield
(1, 1+23, 123)-Net in Base 25 — Upper bound on s
There is no (1, 24, 124)-net in base 25, because
- 15 times m-reduction [i] would yield (1, 9, 124)-net in base 25, but
- extracting embedded orthogonal array [i] would yield OA(259, 124, S25, 8), but
- the linear programming bound shows that M ≥ 119725 208199 920654 296875 / 31015 449154 > 259 [i]
- extracting embedded orthogonal array [i] would yield OA(259, 124, S25, 8), but