Best Known (43, 66, s)-Nets in Base 64
(43, 66, 882)-Net over F64 — Constructive and digital
Digital (43, 66, 882)-net over F64, using
- net defined by OOA [i] based on linear OOA(6466, 882, F64, 23, 23) (dual of [(882, 23), 20220, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6466, 9703, F64, 23) (dual of [9703, 9637, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6466, 9709, F64, 23) (dual of [9709, 9643, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6466, 9703, F64, 23) (dual of [9703, 9637, 24]-code), using
(43, 66, 5959)-Net in Base 64 — Constructive
(43, 66, 5959)-net in base 64, using
- net defined by OOA [i] based on OOA(6466, 5959, S64, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6466, 65550, S64, 23), using
- 2 times code embedding in larger space [i] based on OA(6464, 65548, S64, 23), using
- discarding parts of the base [i] based on linear OA(25648, 65548, F256, 23) (dual of [65548, 65500, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(25648, 65548, F256, 23) (dual of [65548, 65500, 24]-code), using
- 2 times code embedding in larger space [i] based on OA(6464, 65548, S64, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(6466, 65550, S64, 23), using
(43, 66, 37686)-Net over F64 — Digital
Digital (43, 66, 37686)-net over F64, using
(43, 66, large)-Net in Base 64 — Upper bound on s
There is no (43, 66, large)-net in base 64, because
- 21 times m-reduction [i] would yield (43, 45, large)-net in base 64, but