Best Known (54−19, 54, s)-Nets in Base 64
(54−19, 54, 1078)-Net over F64 — Constructive and digital
Digital (35, 54, 1078)-net over F64, using
- net defined by OOA [i] based on linear OOA(6454, 1078, F64, 19, 19) (dual of [(1078, 19), 20428, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6454, 9703, F64, 19) (dual of [9703, 9649, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6454, 9709, F64, 19) (dual of [9709, 9655, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6454, 9703, F64, 19) (dual of [9703, 9649, 20]-code), using
(54−19, 54, 7283)-Net in Base 64 — Constructive
(35, 54, 7283)-net in base 64, using
- net defined by OOA [i] based on OOA(6454, 7283, S64, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(6454, 65548, S64, 19), using
- discarding parts of the base [i] based on linear OA(25640, 65548, F256, 19) (dual of [65548, 65508, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- 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(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,9]) ⊂ C([0,7]) [i] based on
- discarding parts of the base [i] based on linear OA(25640, 65548, F256, 19) (dual of [65548, 65508, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on OA(6454, 65548, S64, 19), using
(54−19, 54, 31438)-Net over F64 — Digital
Digital (35, 54, 31438)-net over F64, using
(54−19, 54, large)-Net in Base 64 — Upper bound on s
There is no (35, 54, large)-net in base 64, because
- 17 times m-reduction [i] would yield (35, 37, large)-net in base 64, but