Best Known (55, 55+40, s)-Nets in Base 25
(55, 55+40, 326)-Net over F25 — Constructive and digital
Digital (55, 95, 326)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 30, 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, 65, 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, 30, 126)-net over F25, using
(55, 55+40, 1651)-Net over F25 — Digital
Digital (55, 95, 1651)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2595, 1651, F25, 40) (dual of [1651, 1556, 41]-code), using
- 1555 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) [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]
- 1555 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) [i] based on linear OA(2540, 41, F25, 40) (dual of [41, 1, 41]-code or 41-arc in PG(39,25)), using
(55, 55+40, 1511148)-Net in Base 25 — Upper bound on s
There is no (55, 95, 1511149)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 6 372434 401933 417602 119501 722759 064042 497096 164971 372334 356996 920236 567275 983109 913745 099534 331951 482487 927907 663076 264180 513517 687521 > 2595 [i]