Best Known (36, 36+34, s)-Nets in Base 25
(36, 36+34, 230)-Net over F25 — Constructive and digital
Digital (36, 70, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 26, 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, 44, 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, 26, 104)-net over F25, using
(36, 36+34, 536)-Net over F25 — Digital
Digital (36, 70, 536)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2570, 536, F25, 34) (dual of [536, 466, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2570, 645, F25, 34) (dual of [645, 575, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(26) [i] based on
- linear OA(2564, 625, F25, 34) (dual of [625, 561, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(256, 20, F25, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- construction X applied to Ce(33) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2570, 645, F25, 34) (dual of [645, 575, 35]-code), using
(36, 36+34, 170582)-Net in Base 25 — Upper bound on s
There is no (36, 70, 170583)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 71 747570 683634 781415 203505 104906 031649 601267 874693 956279 142366 874645 848865 791855 028400 886600 721065 > 2570 [i]