Best Known (86−24, 86, s)-Nets in Base 32
(86−24, 86, 2795)-Net over F32 — Constructive and digital
Digital (62, 86, 2795)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (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 (3, 15, 64)-net over F32, using
(86−24, 86, 21845)-Net in Base 32 — Constructive
(62, 86, 21845)-net in base 32, using
- 322 times duplication [i] based on (60, 84, 21845)-net in base 32, using
- base change [i] based on digital (46, 70, 21845)-net over F64, using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- base change [i] based on digital (46, 70, 21845)-net over F64, using
(86−24, 86, 129147)-Net over F32 — Digital
Digital (62, 86, 129147)-net over F32, using
(86−24, 86, large)-Net in Base 32 — Upper bound on s
There is no (62, 86, large)-net in base 32, because
- 22 times m-reduction [i] would yield (62, 64, large)-net in base 32, but