Best Known (60, 84, s)-Nets in Base 32
(60, 84, 2775)-Net over F32 — Constructive and digital
Digital (60, 84, 2775)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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 (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 (1, 13, 44)-net over F32, using
(60, 84, 21845)-Net in Base 32 — Constructive
(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
(60, 84, 95547)-Net over F32 — Digital
Digital (60, 84, 95547)-net over F32, using
(60, 84, 97206)-Net in Base 32
(60, 84, 97206)-net in base 32, using
- base change [i] based on digital (46, 70, 97206)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6470, 97206, F64, 2, 24) (dual of [(97206, 2), 194342, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6470, 131073, F64, 2, 24) (dual of [(131073, 2), 262076, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6470, 262146, F64, 24) (dual of [262146, 262076, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [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(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- OOA 2-folding [i] based on linear OA(6470, 262146, F64, 24) (dual of [262146, 262076, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(6470, 131073, F64, 2, 24) (dual of [(131073, 2), 262076, 25]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6470, 97206, F64, 2, 24) (dual of [(97206, 2), 194342, 25]-NRT-code), using
(60, 84, large)-Net in Base 32 — Upper bound on s
There is no (60, 84, large)-net in base 32, because
- 22 times m-reduction [i] would yield (60, 62, large)-net in base 32, but