Best Known (92, 119, s)-Nets in Base 8
(92, 119, 2521)-Net over F8 — Constructive and digital
Digital (92, 119, 2521)-net over F8, using
- 82 times duplication [i] based on digital (90, 117, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8117, 2521, F8, 27, 27) (dual of [(2521, 27), 67950, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8117, 32779, F8, 27) (dual of [32779, 32662, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8117, 32774, F8, 27) (dual of [32774, 32657, 28]-code), using
- net defined by OOA [i] based on linear OOA(8117, 2521, F8, 27, 27) (dual of [(2521, 27), 67950, 28]-NRT-code), using
(92, 119, 26599)-Net over F8 — Digital
Digital (92, 119, 26599)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8119, 26599, F8, 27) (dual of [26599, 26480, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8119, 32782, F8, 27) (dual of [32782, 32663, 28]-code), using
- construction XX applied to Ce(26) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(81, 12, F8, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(26) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8119, 32782, F8, 27) (dual of [32782, 32663, 28]-code), using
(92, 119, large)-Net in Base 8 — Upper bound on s
There is no (92, 119, large)-net in base 8, because
- 25 times m-reduction [i] would yield (92, 94, large)-net in base 8, but