Best Known (122, 122+35, s)-Nets in Base 8
(122, 122+35, 1929)-Net over F8 — Constructive and digital
Digital (122, 157, 1929)-net over F8, using
- net defined by OOA [i] based on linear OOA(8157, 1929, F8, 35, 35) (dual of [(1929, 35), 67358, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(8157, 32794, F8, 35) (dual of [32794, 32637, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(86, 26, F8, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- OOA 17-folding and stacking with additional row [i] based on linear OA(8157, 32794, F8, 35) (dual of [32794, 32637, 36]-code), using
(122, 122+35, 32794)-Net over F8 — Digital
Digital (122, 157, 32794)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8157, 32794, F8, 35) (dual of [32794, 32637, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(86, 26, F8, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
(122, 122+35, large)-Net in Base 8 — Upper bound on s
There is no (122, 157, large)-net in base 8, because
- 33 times m-reduction [i] would yield (122, 124, large)-net in base 8, but