Best Known (75, 75+18, s)-Nets in Base 8
(75, 75+18, 29128)-Net over F8 — Constructive and digital
Digital (75, 93, 29128)-net over F8, using
- net defined by OOA [i] based on linear OOA(893, 29128, F8, 18, 18) (dual of [(29128, 18), 524211, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(893, 262152, F8, 18) (dual of [262152, 262059, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(893, 262153, F8, 18) (dual of [262153, 262060, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(893, 262153, F8, 18) (dual of [262153, 262060, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(893, 262152, F8, 18) (dual of [262152, 262059, 19]-code), using
(75, 75+18, 151419)-Net over F8 — Digital
Digital (75, 93, 151419)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(893, 151419, F8, 18) (dual of [151419, 151326, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(893, 262153, F8, 18) (dual of [262153, 262060, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(891, 262144, F8, 18) (dual of [262144, 262053, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(893, 262153, F8, 18) (dual of [262153, 262060, 19]-code), using
(75, 75+18, large)-Net in Base 8 — Upper bound on s
There is no (75, 93, large)-net in base 8, because
- 16 times m-reduction [i] would yield (75, 77, large)-net in base 8, but