Best Known (80−77, 80, s)-Nets in Base 25
(80−77, 80, 52)-Net over F25 — Constructive and digital
Digital (3, 80, 52)-net over F25, 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
(80−77, 80, 56)-Net over F25 — Digital
Digital (3, 80, 56)-net over F25, 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
(80−77, 80, 102)-Net over F25 — Upper bound on s (digital)
There is no digital (3, 80, 103)-net over F25, because
- 2 times m-reduction [i] would yield digital (3, 78, 103)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(2578, 103, F25, 75) (dual of [103, 25, 76]-code), but
- residual code [i] would yield OA(253, 27, S25, 3), but
- extracting embedded orthogonal array [i] would yield linear OA(2578, 103, F25, 75) (dual of [103, 25, 76]-code), but
(80−77, 80, 171)-Net in Base 25 — Upper bound on s
There is no (3, 80, 172)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2580, 172, S25, 77), but
- the linear programming bound shows that M ≥ 10 840076 257569 507317 773720 236737 255415 425862 758503 753156 628970 950332 553138 960619 426614 699688 064813 454246 859691 920690 238475 799560 546875 / 1561 904162 748023 191819 > 2580 [i]