Best Known (128, 162, s)-Nets in Base 8
(128, 162, 1931)-Net over F8 — Constructive and digital
Digital (128, 162, 1931)-net over F8, using
- net defined by OOA [i] based on linear OOA(8162, 1931, F8, 34, 34) (dual of [(1931, 34), 65492, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(8162, 32827, F8, 34) (dual of [32827, 32665, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(8162, 32829, F8, 34) (dual of [32829, 32667, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(22) [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(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(816, 61, F8, 10) (dual of [61, 45, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-code), using
- construction X applied to Ce(33) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8162, 32829, F8, 34) (dual of [32829, 32667, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(8162, 32827, F8, 34) (dual of [32827, 32665, 35]-code), using
(128, 162, 51021)-Net over F8 — Digital
Digital (128, 162, 51021)-net over F8, using
(128, 162, large)-Net in Base 8 — Upper bound on s
There is no (128, 162, large)-net in base 8, because
- 32 times m-reduction [i] would yield (128, 130, large)-net in base 8, but