Best Known (134−21, 134, s)-Nets in Base 8
(134−21, 134, 209719)-Net over F8 — Constructive and digital
Digital (113, 134, 209719)-net over F8, using
- net defined by OOA [i] based on linear OOA(8134, 209719, F8, 21, 21) (dual of [(209719, 21), 4403965, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8134, 2097191, F8, 21) (dual of [2097191, 2097057, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8134, 2097191, F8, 21) (dual of [2097191, 2097057, 22]-code), using
(134−21, 134, 2097194)-Net over F8 — Digital
Digital (113, 134, 2097194)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8134, 2097194, F8, 21) (dual of [2097194, 2097060, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(8127, 2097152, F8, 21) (dual of [2097152, 2097025, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
(134−21, 134, large)-Net in Base 8 — Upper bound on s
There is no (113, 134, large)-net in base 8, because
- 19 times m-reduction [i] would yield (113, 115, large)-net in base 8, but