Best Known (169−33, 169, s)-Nets in Base 8
(169−33, 169, 16384)-Net over F8 — Constructive and digital
Digital (136, 169, 16384)-net over F8, using
- net defined by OOA [i] based on linear OOA(8169, 16384, F8, 33, 33) (dual of [(16384, 33), 540503, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [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]
- OOA 16-folding and stacking with additional row [i] based on linear OA(8169, 262145, F8, 33) (dual of [262145, 261976, 34]-code), using
(169−33, 169, 139008)-Net over F8 — Digital
Digital (136, 169, 139008)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8169, 139008, F8, 33) (dual of [139008, 138839, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, 262144, F8, 33) (dual of [262144, 261975, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(8169, 262144, F8, 33) (dual of [262144, 261975, 34]-code), using
(169−33, 169, large)-Net in Base 8 — Upper bound on s
There is no (136, 169, large)-net in base 8, because
- 31 times m-reduction [i] would yield (136, 138, large)-net in base 8, but