Best Known (126−29, 126, s)-Nets in Base 8
(126−29, 126, 2340)-Net over F8 — Constructive and digital
Digital (97, 126, 2340)-net over F8, using
- net defined by OOA [i] based on linear OOA(8126, 2340, F8, 29, 29) (dual of [(2340, 29), 67734, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8126, 32761, F8, 29) (dual of [32761, 32635, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8126, 32761, F8, 29) (dual of [32761, 32635, 30]-code), using
(126−29, 126, 23658)-Net over F8 — Digital
Digital (97, 126, 23658)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8126, 23658, F8, 29) (dual of [23658, 23532, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
(126−29, 126, large)-Net in Base 8 — Upper bound on s
There is no (97, 126, large)-net in base 8, because
- 27 times m-reduction [i] would yield (97, 99, large)-net in base 8, but