Best Known (33, 33+28, s)-Nets in Base 25
(33, 33+28, 230)-Net over F25 — Constructive and digital
Digital (33, 61, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (10, 38, 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 (9, 23, 104)-net over F25, using
(33, 33+28, 708)-Net over F25 — Digital
Digital (33, 61, 708)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2561, 708, F25, 28) (dual of [708, 647, 29]-code), using
- 72 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 35 times 0) [i] based on linear OA(2552, 627, F25, 28) (dual of [627, 575, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(2552, 625, F25, 28) (dual of [625, 573, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2550, 625, F25, 27) (dual of [625, 575, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- 72 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 35 times 0) [i] based on linear OA(2552, 627, F25, 28) (dual of [627, 575, 29]-code), using
(33, 33+28, 310642)-Net in Base 25 — Upper bound on s
There is no (33, 61, 310643)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 18 808305 634266 285670 265227 493404 886563 223498 287848 335736 014603 303291 339805 974174 120305 > 2561 [i]