Best Known (46, 46+13, s)-Nets in Base 8
(46, 46+13, 5464)-Net over F8 — Constructive and digital
Digital (46, 59, 5464)-net over F8, using
- net defined by OOA [i] based on linear OOA(859, 5464, F8, 13, 13) (dual of [(5464, 13), 70973, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(859, 32785, F8, 13) (dual of [32785, 32726, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(859, 32786, F8, 13) (dual of [32786, 32727, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(841, 32768, F8, 10) (dual of [32768, 32727, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(859, 32786, F8, 13) (dual of [32786, 32727, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(859, 32785, F8, 13) (dual of [32785, 32726, 14]-code), using
(46, 46+13, 32786)-Net over F8 — Digital
Digital (46, 59, 32786)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(859, 32786, F8, 13) (dual of [32786, 32727, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(841, 32768, F8, 10) (dual of [32768, 32727, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(83, 18, F8, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
(46, 46+13, large)-Net in Base 8 — Upper bound on s
There is no (46, 59, large)-net in base 8, because
- 11 times m-reduction [i] would yield (46, 48, large)-net in base 8, but