Best Known (154−34, 154, s)-Nets in Base 8
(154−34, 154, 1929)-Net over F8 — Constructive and digital
Digital (120, 154, 1929)-net over F8, using
- 82 times duplication [i] based on digital (118, 152, 1929)-net over F8, using
- net defined by OOA [i] based on linear OOA(8152, 1929, F8, 34, 34) (dual of [(1929, 34), 65434, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8152, 32793, F8, 34) (dual of [32793, 32641, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 32794, F8, 34) (dual of [32794, 32642, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [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(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(33) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 32794, F8, 34) (dual of [32794, 32642, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8152, 32793, F8, 34) (dual of [32793, 32641, 35]-code), using
- net defined by OOA [i] based on linear OOA(8152, 1929, F8, 34, 34) (dual of [(1929, 34), 65434, 35]-NRT-code), using
(154−34, 154, 32802)-Net over F8 — Digital
Digital (120, 154, 32802)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8154, 32802, F8, 34) (dual of [32802, 32648, 35]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8153, 32800, F8, 34) (dual of [32800, 32647, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [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(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- linear OA(8153, 32801, F8, 33) (dual of [32801, 32648, 34]-code), using Gilbert–Varšamov bound and bm = 8153 > Vbs−1(k−1) = 13317 405964 692389 354584 712266 720809 857610 765817 395742 461213 286689 165189 144404 800715 365234 669179 652157 476874 453353 685012 404430 231564 190720 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(8153, 32800, F8, 34) (dual of [32800, 32647, 35]-code), using
- construction X with Varšamov bound [i] based on
(154−34, 154, large)-Net in Base 8 — Upper bound on s
There is no (120, 154, large)-net in base 8, because
- 32 times m-reduction [i] would yield (120, 122, large)-net in base 8, but