Best Known (141, 141+30, s)-Nets in Base 8
(141, 141+30, 17480)-Net over F8 — Constructive and digital
Digital (141, 171, 17480)-net over F8, using
- net defined by OOA [i] based on linear OOA(8171, 17480, F8, 30, 30) (dual of [(17480, 30), 524229, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(8171, 262200, F8, 30) (dual of [262200, 262029, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8171, 262206, F8, 30) (dual of [262206, 262035, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- linear OA(8157, 262144, F8, 30) (dual of [262144, 261987, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(814, 62, F8, 8) (dual of [62, 48, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(814, 63, F8, 8) (dual of [63, 49, 9]-code), using
- construction X applied to Ce(29) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(8171, 262206, F8, 30) (dual of [262206, 262035, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(8171, 262200, F8, 30) (dual of [262200, 262029, 31]-code), using
(141, 141+30, 352499)-Net over F8 — Digital
Digital (141, 171, 352499)-net over F8, using
(141, 141+30, large)-Net in Base 8 — Upper bound on s
There is no (141, 171, large)-net in base 8, because
- 28 times m-reduction [i] would yield (141, 143, large)-net in base 8, but