Best Known (74, 74+29, s)-Nets in Base 32
(74, 74+29, 2405)-Net over F32 — Constructive and digital
Digital (74, 103, 2405)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 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 (57, 86, 2341)-net over F32, using
- net defined by OOA [i] based on linear OOA(3286, 2341, F32, 29, 29) (dual of [(2341, 29), 67803, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3286, 32775, F32, 29) (dual of [32775, 32689, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3286, 32776, F32, 29) (dual of [32776, 32690, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(3285, 32769, F32, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [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 C([0,14]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3286, 32776, F32, 29) (dual of [32776, 32690, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3286, 32775, F32, 29) (dual of [32775, 32689, 30]-code), using
- net defined by OOA [i] based on linear OOA(3286, 2341, F32, 29, 29) (dual of [(2341, 29), 67803, 30]-NRT-code), using
- digital (3, 17, 64)-net over F32, using
(74, 74+29, 18724)-Net in Base 32 — Constructive
(74, 103, 18724)-net in base 32, using
- 321 times duplication [i] based on (73, 102, 18724)-net in base 32, using
- base change [i] based on digital (56, 85, 18724)-net over F64, using
- net defined by OOA [i] based on linear OOA(6485, 18724, F64, 29, 29) (dual of [(18724, 29), 542911, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6485, 262137, F64, 29) (dual of [262137, 262052, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(6485, 262144, F64, 29) (dual of [262144, 262059, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(6485, 262144, F64, 29) (dual of [262144, 262059, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6485, 262137, F64, 29) (dual of [262137, 262052, 30]-code), using
- net defined by OOA [i] based on linear OOA(6485, 18724, F64, 29, 29) (dual of [(18724, 29), 542911, 30]-NRT-code), using
- base change [i] based on digital (56, 85, 18724)-net over F64, using
(74, 74+29, 125457)-Net over F32 — Digital
Digital (74, 103, 125457)-net over F32, using
(74, 74+29, large)-Net in Base 32 — Upper bound on s
There is no (74, 103, large)-net in base 32, because
- 27 times m-reduction [i] would yield (74, 76, large)-net in base 32, but