Best Known (142, 142+29, s)-Nets in Base 8
(142, 142+29, 37449)-Net over F8 — Constructive and digital
Digital (142, 171, 37449)-net over F8, using
- 81 times duplication [i] based on digital (141, 170, 37449)-net over F8, using
- net defined by OOA [i] based on linear OOA(8170, 37449, F8, 29, 29) (dual of [(37449, 29), 1085851, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8170, 524287, F8, 29) (dual of [524287, 524117, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8170, 524290, F8, 29) (dual of [524290, 524120, 30]-code), using
- trace code [i] based on linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- trace code [i] based on linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8170, 524290, F8, 29) (dual of [524290, 524120, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8170, 524287, F8, 29) (dual of [524287, 524117, 30]-code), using
- net defined by OOA [i] based on linear OOA(8170, 37449, F8, 29, 29) (dual of [(37449, 29), 1085851, 30]-NRT-code), using
(142, 142+29, 528711)-Net over F8 — Digital
Digital (142, 171, 528711)-net over F8, using
(142, 142+29, large)-Net in Base 8 — Upper bound on s
There is no (142, 171, large)-net in base 8, because
- 27 times m-reduction [i] would yield (142, 144, large)-net in base 8, but