Best Known (63, 63+14, s)-Nets in Base 2
(63, 63+14, 292)-Net over F2 — Constructive and digital
Digital (63, 77, 292)-net over F2, using
- net defined by OOA [i] based on linear OOA(277, 292, F2, 14, 14) (dual of [(292, 14), 4011, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(277, 2044, F2, 14) (dual of [2044, 1967, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(277, 2047, F2, 14) (dual of [2047, 1970, 15]-code), using
- 1 times truncation [i] based on linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(277, 2047, F2, 14) (dual of [2047, 1970, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(277, 2044, F2, 14) (dual of [2044, 1967, 15]-code), using
(63, 63+14, 682)-Net over F2 — Digital
Digital (63, 77, 682)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(277, 682, F2, 3, 14) (dual of [(682, 3), 1969, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(277, 2046, F2, 14) (dual of [2046, 1969, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(277, 2047, F2, 14) (dual of [2047, 1970, 15]-code), using
- 1 times truncation [i] based on linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 1 times truncation [i] based on linear OA(278, 2048, F2, 15) (dual of [2048, 1970, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(277, 2047, F2, 14) (dual of [2047, 1970, 15]-code), using
- OOA 3-folding [i] based on linear OA(277, 2046, F2, 14) (dual of [2046, 1969, 15]-code), using
(63, 63+14, 6912)-Net in Base 2 — Upper bound on s
There is no (63, 77, 6913)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 151226 184839 500083 124352 > 277 [i]