Best Known (87−84, 87, s)-Nets in Base 25
(87−84, 87, 52)-Net over F25 — Constructive and digital
Digital (3, 87, 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
(87−84, 87, 56)-Net over F25 — Digital
Digital (3, 87, 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
(87−84, 87, 102)-Net over F25 — Upper bound on s (digital)
There is no digital (3, 87, 103)-net over F25, because
- 9 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
(87−84, 87, 126)-Net in Base 25 — Upper bound on s
There is no (3, 87, 127)-net in base 25, because
- extracting embedded orthogonal array [i] would yield OA(2587, 127, S25, 84), but
- the linear programming bound shows that M ≥ 105 918506 667553 724288 562000 015746 935625 841393 533988 749405 211346 917829 452202 563149 822860 222412 819475 312772 965480 689890 682697 296142 578125 / 2 518936 507087 > 2587 [i]