Best Known (128, 128+30, s)-Nets in Base 8
(128, 128+30, 17477)-Net over F8 — Constructive and digital
Digital (128, 158, 17477)-net over F8, using
- net defined by OOA [i] based on linear OOA(8158, 17477, F8, 30, 30) (dual of [(17477, 30), 524152, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8158, 262155, F8, 30) (dual of [262155, 261997, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 262157, F8, 30) (dual of [262157, 261999, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8158, 262157, F8, 30) (dual of [262157, 261999, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8158, 262155, F8, 30) (dual of [262155, 261997, 31]-code), using
(128, 128+30, 186905)-Net over F8 — Digital
Digital (128, 158, 186905)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8158, 186905, F8, 30) (dual of [186905, 186747, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8158, 262157, F8, 30) (dual of [262157, 261999, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(8158, 262157, F8, 30) (dual of [262157, 261999, 31]-code), using
(128, 128+30, large)-Net in Base 8 — Upper bound on s
There is no (128, 158, large)-net in base 8, because
- 28 times m-reduction [i] would yield (128, 130, large)-net in base 8, but