Best Known (84−25, 84, s)-Nets in Base 64
(84−25, 84, 21849)-Net over F64 — Constructive and digital
Digital (59, 84, 21849)-net over F64, using
- net defined by OOA [i] based on linear OOA(6484, 21849, F64, 25, 25) (dual of [(21849, 25), 546141, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6484, 262189, F64, 25) (dual of [262189, 262105, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6484, 262192, F64, 25) (dual of [262192, 262108, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- linear OA(6473, 262145, F64, 25) (dual of [262145, 262072, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6411, 47, F64, 11) (dual of [47, 36, 12]-code or 47-arc in PG(10,64)), using
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
- Reed–Solomon code RS(53,64) [i]
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
- construction X applied to C([0,12]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6484, 262192, F64, 25) (dual of [262192, 262108, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6484, 262189, F64, 25) (dual of [262189, 262105, 26]-code), using
(84−25, 84, 326338)-Net over F64 — Digital
Digital (59, 84, 326338)-net over F64, using
(84−25, 84, large)-Net in Base 64 — Upper bound on s
There is no (59, 84, large)-net in base 64, because
- 23 times m-reduction [i] would yield (59, 61, large)-net in base 64, but