Best Known (29, 38, s)-Nets in Base 8
(29, 38, 8194)-Net over F8 — Constructive and digital
Digital (29, 38, 8194)-net over F8, using
- net defined by OOA [i] based on linear OOA(838, 8194, F8, 9, 9) (dual of [(8194, 9), 73708, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(838, 32777, F8, 9) (dual of [32777, 32739, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(8) ⊂ Ce(5) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(838, 32777, F8, 9) (dual of [32777, 32739, 10]-code), using
(29, 38, 28658)-Net over F8 — Digital
Digital (29, 38, 28658)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(838, 28658, F8, 9) (dual of [28658, 28620, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(838, 32777, F8, 9) (dual of [32777, 32739, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(8) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(838, 32777, F8, 9) (dual of [32777, 32739, 10]-code), using
(29, 38, large)-Net in Base 8 — Upper bound on s
There is no (29, 38, large)-net in base 8, because
- 7 times m-reduction [i] would yield (29, 31, large)-net in base 8, but