Best Known (99−24, 99, s)-Nets in Base 32
(99−24, 99, 87384)-Net over F32 — Constructive and digital
Digital (75, 99, 87384)-net over F32, using
- net defined by OOA [i] based on linear OOA(3299, 87384, F32, 24, 24) (dual of [(87384, 24), 2097117, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3299, 1048608, F32, 24) (dual of [1048608, 1048509, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3299, 1048609, F32, 24) (dual of [1048609, 1048510, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3299, 1048609, F32, 24) (dual of [1048609, 1048510, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3299, 1048608, F32, 24) (dual of [1048608, 1048509, 25]-code), using
(99−24, 99, 174763)-Net in Base 32 — Constructive
(75, 99, 174763)-net in base 32, using
- net defined by OOA [i] based on OOA(3299, 174763, S32, 24, 24), using
- OA 12-folding and stacking [i] based on OA(3299, 2097156, S32, 24), using
- 1 times code embedding in larger space [i] based on OA(3298, 2097155, S32, 24), using
- discarding parts of the base [i] based on linear OA(12870, 2097155, F128, 24) (dual of [2097155, 2097085, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(12870, 2097155, F128, 24) (dual of [2097155, 2097085, 25]-code), using
- 1 times code embedding in larger space [i] based on OA(3298, 2097155, S32, 24), using
- OA 12-folding and stacking [i] based on OA(3299, 2097156, S32, 24), using
(99−24, 99, 1048609)-Net over F32 — Digital
Digital (75, 99, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3299, 1048609, F32, 24) (dual of [1048609, 1048510, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
(99−24, 99, large)-Net in Base 32 — Upper bound on s
There is no (75, 99, large)-net in base 32, because
- 22 times m-reduction [i] would yield (75, 77, large)-net in base 32, but