Best Known (18, 18+9, s)-Nets in Base 64
(18, 18+9, 65538)-Net over F64 — Constructive and digital
Digital (18, 27, 65538)-net over F64, using
- net defined by OOA [i] based on linear OOA(6427, 65538, F64, 9, 9) (dual of [(65538, 9), 589815, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6427, 262153, F64, 9) (dual of [262153, 262126, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(6427, 262155, F64, 9) (dual of [262155, 262128, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(6427, 262155, F64, 9) (dual of [262155, 262128, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6427, 262153, F64, 9) (dual of [262153, 262126, 10]-code), using
(18, 18+9, 262155)-Net over F64 — Digital
Digital (18, 27, 262155)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6427, 262155, F64, 9) (dual of [262155, 262128, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
(18, 18+9, large)-Net in Base 64 — Upper bound on s
There is no (18, 27, large)-net in base 64, because
- 7 times m-reduction [i] would yield (18, 20, large)-net in base 64, but