Best Known (116, 116+34, s)-Nets in Base 8
(116, 116+34, 1928)-Net over F8 — Constructive and digital
Digital (116, 150, 1928)-net over F8, using
- 82 times duplication [i] based on digital (114, 148, 1928)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 1928, F8, 34, 34) (dual of [(1928, 34), 65404, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8148, 32776, F8, 34) (dual of [32776, 32628, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 32777, F8, 34) (dual of [32777, 32629, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(30) [i] based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(33) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 32777, F8, 34) (dual of [32777, 32629, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8148, 32776, F8, 34) (dual of [32776, 32628, 35]-code), using
- net defined by OOA [i] based on linear OOA(8148, 1928, F8, 34, 34) (dual of [(1928, 34), 65404, 35]-NRT-code), using
(116, 116+34, 29276)-Net over F8 — Digital
Digital (116, 150, 29276)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8150, 29276, F8, 34) (dual of [29276, 29126, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8150, 32787, F8, 34) (dual of [32787, 32637, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(8146, 32768, F8, 34) (dual of [32768, 32622, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8131, 32768, F8, 30) (dual of [32768, 32637, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(8150, 32787, F8, 34) (dual of [32787, 32637, 35]-code), using
(116, 116+34, large)-Net in Base 8 — Upper bound on s
There is no (116, 150, large)-net in base 8, because
- 32 times m-reduction [i] would yield (116, 118, large)-net in base 8, but