Best Known (127, 127+30, s)-Nets in Base 8
(127, 127+30, 17476)-Net over F8 — Constructive and digital
Digital (127, 157, 17476)-net over F8, using
- net defined by OOA [i] based on linear OOA(8157, 17476, F8, 30, 30) (dual of [(17476, 30), 524123, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8157, 262140, F8, 30) (dual of [262140, 261983, 31]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8157, 262140, F8, 30) (dual of [262140, 261983, 31]-code), using
(127, 127+30, 173527)-Net over F8 — Digital
Digital (127, 157, 173527)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8157, 173527, F8, 30) (dual of [173527, 173370, 31]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using
(127, 127+30, large)-Net in Base 8 — Upper bound on s
There is no (127, 157, large)-net in base 8, because
- 28 times m-reduction [i] would yield (127, 129, large)-net in base 8, but