Best Known (43, 43+14, s)-Nets in Base 32
(43, 43+14, 149800)-Net over F32 — Constructive and digital
Digital (43, 57, 149800)-net over F32, using
- net defined by OOA [i] based on linear OOA(3257, 149800, F32, 14, 14) (dual of [(149800, 14), 2097143, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3257, 1048600, F32, 14) (dual of [1048600, 1048543, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(3253, 1048576, F32, 14) (dual of [1048576, 1048523, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3233, 1048576, F32, 9) (dual of [1048576, 1048543, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- OA 7-folding and stacking [i] based on linear OA(3257, 1048600, F32, 14) (dual of [1048600, 1048543, 15]-code), using
(43, 43+14, 299593)-Net in Base 32 — Constructive
(43, 57, 299593)-net in base 32, using
- 321 times duplication [i] based on (42, 56, 299593)-net in base 32, using
- base change [i] based on digital (26, 40, 299593)-net over F128, using
- net defined by OOA [i] based on linear OOA(12840, 299593, F128, 14, 14) (dual of [(299593, 14), 4194262, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12840, 2097151, F128, 14) (dual of [2097151, 2097111, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12840, 2097151, F128, 14) (dual of [2097151, 2097111, 15]-code), using
- net defined by OOA [i] based on linear OOA(12840, 299593, F128, 14, 14) (dual of [(299593, 14), 4194262, 15]-NRT-code), using
- base change [i] based on digital (26, 40, 299593)-net over F128, using
(43, 43+14, 1048600)-Net over F32 — Digital
Digital (43, 57, 1048600)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3257, 1048600, F32, 14) (dual of [1048600, 1048543, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(3253, 1048576, F32, 14) (dual of [1048576, 1048523, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3233, 1048576, F32, 9) (dual of [1048576, 1048543, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
(43, 43+14, large)-Net in Base 32 — Upper bound on s
There is no (43, 57, large)-net in base 32, because
- 12 times m-reduction [i] would yield (43, 45, large)-net in base 32, but