Best Known (27, 27+15, s)-Nets in Base 64
(27, 27+15, 1386)-Net over F64 — Constructive and digital
Digital (27, 42, 1386)-net over F64, using
- net defined by OOA [i] based on linear OOA(6442, 1386, F64, 15, 15) (dual of [(1386, 15), 20748, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6442, 9703, F64, 15) (dual of [9703, 9661, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6442, 9709, F64, 15) (dual of [9709, 9667, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6442, 9703, F64, 15) (dual of [9703, 9661, 16]-code), using
(27, 27+15, 9363)-Net in Base 64 — Constructive
(27, 42, 9363)-net in base 64, using
- 642 times duplication [i] based on (25, 40, 9363)-net in base 64, using
- base change [i] based on digital (15, 30, 9363)-net over F256, using
- net defined by OOA [i] based on linear OOA(25630, 9363, F256, 15, 15) (dual of [(9363, 15), 140415, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- 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(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- net defined by OOA [i] based on linear OOA(25630, 9363, F256, 15, 15) (dual of [(9363, 15), 140415, 16]-NRT-code), using
- base change [i] based on digital (15, 30, 9363)-net over F256, using
(27, 27+15, 25164)-Net over F64 — Digital
Digital (27, 42, 25164)-net over F64, using
(27, 27+15, large)-Net in Base 64 — Upper bound on s
There is no (27, 42, large)-net in base 64, because
- 13 times m-reduction [i] would yield (27, 29, large)-net in base 64, but