Best Known (126−24, 126, s)-Nets in Base 8
(126−24, 126, 21845)-Net over F8 — Constructive and digital
Digital (102, 126, 21845)-net over F8, using
- net defined by OOA [i] based on linear OOA(8126, 21845, F8, 24, 24) (dual of [(21845, 24), 524154, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8126, 262140, F8, 24) (dual of [262140, 262014, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 262143, F8, 24) (dual of [262143, 262017, 25]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 262143, F8, 24) (dual of [262143, 262017, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8126, 262140, F8, 24) (dual of [262140, 262014, 25]-code), using
(126−24, 126, 174951)-Net over F8 — Digital
Digital (102, 126, 174951)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8126, 174951, F8, 24) (dual of [174951, 174825, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 262143, F8, 24) (dual of [262143, 262017, 25]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(8127, 262144, F8, 25) (dual of [262144, 262017, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 262143, F8, 24) (dual of [262143, 262017, 25]-code), using
(126−24, 126, large)-Net in Base 8 — Upper bound on s
There is no (102, 126, large)-net in base 8, because
- 22 times m-reduction [i] would yield (102, 104, large)-net in base 8, but