Best Known (112−18, 112, s)-Nets in Base 8
(112−18, 112, 233020)-Net over F8 — Constructive and digital
Digital (94, 112, 233020)-net over F8, using
- net defined by OOA [i] based on linear OOA(8112, 233020, F8, 18, 18) (dual of [(233020, 18), 4194248, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8112, 2097180, F8, 18) (dual of [2097180, 2097068, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8112, 2097186, F8, 18) (dual of [2097186, 2097074, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(86, 34, F8, 4) (dual of [34, 28, 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(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(8112, 2097186, F8, 18) (dual of [2097186, 2097074, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(8112, 2097180, F8, 18) (dual of [2097180, 2097068, 19]-code), using
(112−18, 112, 1789061)-Net over F8 — Digital
Digital (94, 112, 1789061)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8112, 1789061, F8, 18) (dual of [1789061, 1788949, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8112, 2097186, F8, 18) (dual of [2097186, 2097074, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(86, 34, F8, 4) (dual of [34, 28, 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(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(8112, 2097186, F8, 18) (dual of [2097186, 2097074, 19]-code), using
(112−18, 112, large)-Net in Base 8 — Upper bound on s
There is no (94, 112, large)-net in base 8, because
- 16 times m-reduction [i] would yield (94, 96, large)-net in base 8, but