Best Known (46, 69, s)-Nets in Base 64
(46, 69, 23832)-Net over F64 — Constructive and digital
Digital (46, 69, 23832)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 23832, F64, 23, 23) (dual of [(23832, 23), 548067, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6469, 262153, F64, 23) (dual of [262153, 262084, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(6469, 262153, F64, 23) (dual of [262153, 262084, 24]-code), using
(46, 69, 131077)-Net over F64 — Digital
Digital (46, 69, 131077)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6469, 131077, F64, 2, 23) (dual of [(131077, 2), 262085, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6469, 262154, F64, 23) (dual of [262154, 262085, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(6469, 262155, F64, 23) (dual of [262155, 262086, 24]-code), using
- OOA 2-folding [i] based on linear OA(6469, 262154, F64, 23) (dual of [262154, 262085, 24]-code), using
(46, 69, large)-Net in Base 64 — Upper bound on s
There is no (46, 69, large)-net in base 64, because
- 21 times m-reduction [i] would yield (46, 48, large)-net in base 64, but