Best Known (34, 68, s)-Nets in Base 32
(34, 68, 202)-Net over F32 — Constructive and digital
Digital (34, 68, 202)-net over F32, using
- 2 times m-reduction [i] based on digital (34, 70, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (9, 45, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 25, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(34, 68, 288)-Net in Base 32 — Constructive
(34, 68, 288)-net in base 32, using
- t-expansion [i] based on (33, 68, 288)-net in base 32, using
- 16 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 60, 288)-net over F128, using
- 16 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
(34, 68, 570)-Net over F32 — Digital
Digital (34, 68, 570)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3268, 570, F32, 34) (dual of [570, 502, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3268, 1035, F32, 34) (dual of [1035, 967, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(3264, 1024, F32, 34) (dual of [1024, 960, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3257, 1024, F32, 29) (dual of [1024, 967, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(324, 11, F32, 4) (dual of [11, 7, 5]-code or 11-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(3268, 1035, F32, 34) (dual of [1035, 967, 35]-code), using
(34, 68, 242754)-Net in Base 32 — Upper bound on s
There is no (34, 68, 242755)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 239749 165192 492152 190404 542442 997219 771476 374054 167772 889157 493510 049583 728143 738864 892004 626632 802248 > 3268 [i]