Best Known (113−18, 113, s)-Nets in Base 8
(113−18, 113, 233021)-Net over F8 — Constructive and digital
Digital (95, 113, 233021)-net over F8, using
- net defined by OOA [i] based on linear OOA(8113, 233021, F8, 18, 18) (dual of [(233021, 18), 4194265, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(8113, 2097189, F8, 18) (dual of [2097189, 2097076, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [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(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 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(17) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(8113, 2097189, F8, 18) (dual of [2097189, 2097076, 19]-code), using
(113−18, 113, 2037364)-Net over F8 — Digital
Digital (95, 113, 2037364)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8113, 2037364, F8, 18) (dual of [2037364, 2037251, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [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(871, 2097152, F8, 12) (dual of [2097152, 2097081, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(87, 42, F8, 5) (dual of [42, 35, 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(17) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 2097194, F8, 18) (dual of [2097194, 2097081, 19]-code), using
(113−18, 113, large)-Net in Base 8 — Upper bound on s
There is no (95, 113, large)-net in base 8, because
- 16 times m-reduction [i] would yield (95, 97, large)-net in base 8, but