Best Known (168−32, 168, s)-Nets in Base 8
(168−32, 168, 16384)-Net over F8 — Constructive and digital
Digital (136, 168, 16384)-net over F8, using
- net defined by OOA [i] based on linear OOA(8168, 16384, F8, 32, 32) (dual of [(16384, 32), 524120, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(8168, 262144, F8, 32) (dual of [262144, 261976, 33]-code), using
- 1 times truncation [i] based on linear OA(8169, 262145, F8, 33) (dual of [262145, 261976, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(8169, 262145, F8, 33) (dual of [262145, 261976, 34]-code), using
- OA 16-folding and stacking [i] based on linear OA(8168, 262144, F8, 32) (dual of [262144, 261976, 33]-code), using
(168−32, 168, 183167)-Net over F8 — Digital
Digital (136, 168, 183167)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8168, 183167, F8, 32) (dual of [183167, 182999, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(8168, 262144, F8, 32) (dual of [262144, 261976, 33]-code), using
- 1 times truncation [i] based on linear OA(8169, 262145, F8, 33) (dual of [262145, 261976, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(8169, 262145, F8, 33) (dual of [262145, 261976, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8168, 262144, F8, 32) (dual of [262144, 261976, 33]-code), using
(168−32, 168, large)-Net in Base 8 — Upper bound on s
There is no (136, 168, large)-net in base 8, because
- 30 times m-reduction [i] would yield (136, 138, large)-net in base 8, but