Best Known (34, 64, s)-Nets in Base 25
(34, 64, 230)-Net over F25 — Constructive and digital
Digital (34, 64, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 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, 40, 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, 24, 104)-net over F25, using
(34, 64, 645)-Net over F25 — Digital
Digital (34, 64, 645)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2564, 645, F25, 30) (dual of [645, 581, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2564, 648, F25, 30) (dual of [648, 584, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- linear OA(2556, 625, F25, 30) (dual of [625, 569, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2541, 625, F25, 21) (dual of [625, 584, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(258, 23, F25, 8) (dual of [23, 15, 9]-code or 23-arc in PG(7,25)), using
- discarding factors / shortening the dual code based on linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- Reed–Solomon code RS(17,25) [i]
- discarding factors / shortening the dual code based on linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2564, 648, F25, 30) (dual of [648, 584, 31]-code), using
(34, 64, 246652)-Net in Base 25 — Upper bound on s
There is no (34, 64, 246653)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 293877 561174 986803 537329 890465 686817 701648 953413 598130 780476 249926 138186 864674 708980 105865 > 2564 [i]