Best Known (66, 90, s)-Nets in Base 32
(66, 90, 2829)-Net over F32 — Constructive and digital
Digital (66, 90, 2829)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 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 (47, 71, 2731)-net over F32, using
- net defined by OOA [i] based on linear OOA(3271, 2731, F32, 24, 24) (dual of [(2731, 24), 65473, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3271, 32772, F32, 24) (dual of [32772, 32701, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3271, 32775, F32, 24) (dual of [32775, 32704, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] 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]
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3271, 32775, F32, 24) (dual of [32775, 32704, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3271, 32772, F32, 24) (dual of [32772, 32701, 25]-code), using
- net defined by OOA [i] based on linear OOA(3271, 2731, F32, 24, 24) (dual of [(2731, 24), 65473, 25]-NRT-code), using
- digital (7, 19, 98)-net over F32, using
(66, 90, 21847)-Net in Base 32 — Constructive
(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
(66, 90, 235957)-Net over F32 — Digital
Digital (66, 90, 235957)-net over F32, using
(66, 90, large)-Net in Base 32 — Upper bound on s
There is no (66, 90, large)-net in base 32, because
- 22 times m-reduction [i] would yield (66, 68, large)-net in base 32, but