Best Known (173−33, 173, s)-Nets in Base 8
(173−33, 173, 16385)-Net over F8 — Constructive and digital
Digital (140, 173, 16385)-net over F8, using
- net defined by OOA [i] based on linear OOA(8173, 16385, F8, 33, 33) (dual of [(16385, 33), 540532, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8173, 262161, F8, 33) (dual of [262161, 261988, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [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]
- linear OA(8157, 262145, F8, 29) (dual of [262145, 261988, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- OOA 16-folding and stacking with additional row [i] based on linear OA(8173, 262161, F8, 33) (dual of [262161, 261988, 34]-code), using
(173−33, 173, 181795)-Net over F8 — Digital
Digital (140, 173, 181795)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8173, 181795, F8, 33) (dual of [181795, 181622, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(8173, 262161, F8, 33) (dual of [262161, 261988, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [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]
- linear OA(8157, 262145, F8, 29) (dual of [262145, 261988, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8173, 262161, F8, 33) (dual of [262161, 261988, 34]-code), using
(173−33, 173, large)-Net in Base 8 — Upper bound on s
There is no (140, 173, large)-net in base 8, because
- 31 times m-reduction [i] would yield (140, 142, large)-net in base 8, but