Best Known (120, 148, s)-Nets in Base 8
(120, 148, 18726)-Net over F8 — Constructive and digital
Digital (120, 148, 18726)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 18726, F8, 28, 28) (dual of [(18726, 28), 524180, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8148, 262164, F8, 28) (dual of [262164, 262016, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 262165, F8, 28) (dual of [262165, 262017, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 262165, F8, 28) (dual of [262165, 262017, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8148, 262164, F8, 28) (dual of [262164, 262016, 29]-code), using
(120, 148, 192350)-Net over F8 — Digital
Digital (120, 148, 192350)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8148, 192350, F8, 28) (dual of [192350, 192202, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 262165, F8, 28) (dual of [262165, 262017, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(83, 21, F8, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 262165, F8, 28) (dual of [262165, 262017, 29]-code), using
(120, 148, large)-Net in Base 8 — Upper bound on s
There is no (120, 148, large)-net in base 8, because
- 26 times m-reduction [i] would yield (120, 122, large)-net in base 8, but