Best Known (43−10, 43, s)-Nets in Base 8
(43−10, 43, 6555)-Net over F8 — Constructive and digital
Digital (33, 43, 6555)-net over F8, using
- net defined by OOA [i] based on linear OOA(843, 6555, F8, 10, 10) (dual of [(6555, 10), 65507, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(843, 32775, F8, 10) (dual of [32775, 32732, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(843, 32777, F8, 10) (dual of [32777, 32734, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- 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(831, 32768, F8, 7) (dual of [32768, 32737, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(843, 32777, F8, 10) (dual of [32777, 32734, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(843, 32775, F8, 10) (dual of [32775, 32732, 11]-code), using
(43−10, 43, 29632)-Net over F8 — Digital
Digital (33, 43, 29632)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(843, 29632, F8, 10) (dual of [29632, 29589, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(843, 32777, F8, 10) (dual of [32777, 32734, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- 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(831, 32768, F8, 7) (dual of [32768, 32737, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(843, 32777, F8, 10) (dual of [32777, 32734, 11]-code), using
(43−10, 43, large)-Net in Base 8 — Upper bound on s
There is no (33, 43, large)-net in base 8, because
- 8 times m-reduction [i] would yield (33, 35, large)-net in base 8, but