Best Known (59, 59+40, s)-Nets in Base 25
(59, 59+40, 326)-Net over F25 — Constructive and digital
Digital (59, 99, 326)-net over F25, using
- 8 times m-reduction [i] based on digital (59, 107, 326)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 34, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (25, 73, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- digital (10, 34, 126)-net over F25, using
- (u, u+v)-construction [i] based on
(59, 59+40, 2289)-Net over F25 — Digital
Digital (59, 99, 2289)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2599, 2289, F25, 40) (dual of [2289, 2190, 41]-code), using
- 2189 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 30 times 0, 1, 32 times 0, 1, 36 times 0, 1, 38 times 0, 1, 42 times 0, 1, 46 times 0, 1, 50 times 0, 1, 55 times 0, 1, 60 times 0, 1, 64 times 0, 1, 71 times 0, 1, 77 times 0, 1, 83 times 0, 1, 91 times 0, 1, 99 times 0, 1, 107 times 0, 1, 117 times 0, 1, 128 times 0, 1, 138 times 0, 1, 150 times 0, 1, 164 times 0, 1, 178 times 0) [i] based on linear OA(2540, 41, F25, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,25)), using
- dual of repetition code with length 41 [i]
- 2189 step Varšamov–Edel lengthening with (ri) = (3, 2, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 30 times 0, 1, 32 times 0, 1, 36 times 0, 1, 38 times 0, 1, 42 times 0, 1, 46 times 0, 1, 50 times 0, 1, 55 times 0, 1, 60 times 0, 1, 64 times 0, 1, 71 times 0, 1, 77 times 0, 1, 83 times 0, 1, 91 times 0, 1, 99 times 0, 1, 107 times 0, 1, 117 times 0, 1, 128 times 0, 1, 138 times 0, 1, 150 times 0, 1, 164 times 0, 1, 178 times 0) [i] based on linear OA(2540, 41, F25, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,25)), using
(59, 59+40, 2876712)-Net in Base 25 — Upper bound on s
There is no (59, 99, 2876713)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 489213 436019 213642 149087 181624 500634 731416 370226 217763 988125 254877 083061 404836 274483 252858 657345 512273 224103 332197 741615 210287 185737 630305 > 2599 [i]