Best Known (66, 78, s)-Nets in Base 2
(66, 78, 1365)-Net over F2 — Constructive and digital
Digital (66, 78, 1365)-net over F2, using
- net defined by OOA [i] based on linear OOA(278, 1365, F2, 12, 12) (dual of [(1365, 12), 16302, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(278, 8190, F2, 12) (dual of [8190, 8112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(278, 8190, F2, 12) (dual of [8190, 8112, 13]-code), using
(66, 78, 2488)-Net over F2 — Digital
Digital (66, 78, 2488)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(278, 2488, F2, 3, 12) (dual of [(2488, 3), 7386, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(278, 2730, F2, 3, 12) (dual of [(2730, 3), 8112, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(278, 8190, F2, 12) (dual of [8190, 8112, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using
- OOA 3-folding [i] based on linear OA(278, 8190, F2, 12) (dual of [8190, 8112, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(278, 2730, F2, 3, 12) (dual of [(2730, 3), 8112, 13]-NRT-code), using
(66, 78, 24516)-Net in Base 2 — Upper bound on s
There is no (66, 78, 24517)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 302255 761358 084034 092860 > 278 [i]