Best Known (68, 68+24, s)-Nets in Base 32
(68, 68+24, 2838)-Net over F32 — Constructive and digital
Digital (68, 92, 2838)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (10, 22, 108)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (3, 15, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (1, 7, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (46, 70, 2730)-net over F32, using
- net defined by OOA [i] based on linear OOA(3270, 2730, F32, 24, 24) (dual of [(2730, 24), 65450, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3270, 32760, F32, 24) (dual of [32760, 32690, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3270, 32760, F32, 24) (dual of [32760, 32690, 25]-code), using
- net defined by OOA [i] based on linear OOA(3270, 2730, F32, 24, 24) (dual of [(2730, 24), 65450, 25]-NRT-code), using
- digital (10, 22, 108)-net over F32, using
(68, 68+24, 21847)-Net in Base 32 — Constructive
(68, 92, 21847)-net in base 32, using
- 322 times duplication [i] based on (66, 90, 21847)-net in base 32, using
- base change [i] based on digital (51, 75, 21847)-net over F64, using
- net defined by OOA [i] based on linear OOA(6475, 21847, F64, 24, 24) (dual of [(21847, 24), 524253, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(6475, 262164, F64, 24) (dual of [262164, 262089, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(6475, 262167, F64, 24) (dual of [262167, 262092, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(6475, 262167, F64, 24) (dual of [262167, 262092, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(6475, 262164, F64, 24) (dual of [262164, 262089, 25]-code), using
- net defined by OOA [i] based on linear OOA(6475, 21847, F64, 24, 24) (dual of [(21847, 24), 524253, 25]-NRT-code), using
- base change [i] based on digital (51, 75, 21847)-net over F64, using
(68, 68+24, 318941)-Net over F32 — Digital
Digital (68, 92, 318941)-net over F32, using
(68, 68+24, large)-Net in Base 32 — Upper bound on s
There is no (68, 92, large)-net in base 32, because
- 22 times m-reduction [i] would yield (68, 70, large)-net in base 32, but