Best Known (24−11, 24, s)-Nets in Base 64
(24−11, 24, 821)-Net over F64 — Constructive and digital
Digital (13, 24, 821)-net over F64, using
- net defined by OOA [i] based on linear OOA(6424, 821, F64, 11, 11) (dual of [(821, 11), 9007, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6424, 4106, F64, 11) (dual of [4106, 4082, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6424, 4108, F64, 11) (dual of [4108, 4084, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- linear OA(6421, 4097, F64, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6424, 4108, F64, 11) (dual of [4108, 4084, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6424, 4106, F64, 11) (dual of [4106, 4082, 12]-code), using
(24−11, 24, 2714)-Net over F64 — Digital
Digital (13, 24, 2714)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6424, 2714, F64, 11) (dual of [2714, 2690, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6424, 4108, F64, 11) (dual of [4108, 4084, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- linear OA(6421, 4097, F64, 11) (dual of [4097, 4076, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(643, 11, F64, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,64) or 11-cap in PG(2,64)), using
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- Reed–Solomon code RS(61,64) [i]
- discarding factors / shortening the dual code based on linear OA(643, 64, F64, 3) (dual of [64, 61, 4]-code or 64-arc in PG(2,64) or 64-cap in PG(2,64)), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6424, 4108, F64, 11) (dual of [4108, 4084, 12]-code), using
(24−11, 24, large)-Net in Base 64 — Upper bound on s
There is no (13, 24, large)-net in base 64, because
- 9 times m-reduction [i] would yield (13, 15, large)-net in base 64, but