Best Known (10, 14, s)-Nets in Base 32
(10, 14, 524293)-Net over F32 — Constructive and digital
Digital (10, 14, 524293)-net over F32, using
- net defined by OOA [i] based on linear OOA(3214, 524293, F32, 4, 4) (dual of [(524293, 4), 2097158, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1048576, F32, 2) (dual of [1048576, 1048571, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using
(10, 14, 1048577)-Net in Base 32 — Constructive
(10, 14, 1048577)-net in base 32, using
- base change [i] based on digital (6, 10, 1048577)-net over F128, using
- net defined by OOA [i] based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- net defined by OOA [i] based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
(10, 14, 1048586)-Net over F32 — Digital
Digital (10, 14, 1048586)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3214, 1048586, F32, 4) (dual of [1048586, 1048572, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(325, 1048576, F32, 2) (dual of [1048576, 1048571, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
(10, 14, 2097155)-Net in Base 32
(10, 14, 2097155)-net in base 32, using
- base change [i] based on digital (6, 10, 2097155)-net over F128, using
- net defined by OOA [i] based on linear OOA(12810, 2097155, F128, 4, 4) (dual of [(2097155, 4), 8388610, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(12810, 2097155, F128, 3, 4) (dual of [(2097155, 3), 6291455, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- appending kth column [i] based on linear OOA(12810, 2097155, F128, 3, 4) (dual of [(2097155, 3), 6291455, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12810, 2097155, F128, 4, 4) (dual of [(2097155, 4), 8388610, 5]-NRT-code), using
(10, 14, large)-Net in Base 32 — Upper bound on s
There is no (10, 14, large)-net in base 32, because
- 2 times m-reduction [i] would yield (10, 12, large)-net in base 32, but