Best Known (46−16, 46, s)-Nets in Base 64
(46−16, 46, 32768)-Net over F64 — Constructive and digital
Digital (30, 46, 32768)-net over F64, using
- net defined by OOA [i] based on linear OOA(6446, 32768, F64, 16, 16) (dual of [(32768, 16), 524242, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
(46−16, 46, 116753)-Net over F64 — Digital
Digital (30, 46, 116753)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6446, 116753, F64, 2, 16) (dual of [(116753, 2), 233460, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6446, 131073, F64, 2, 16) (dual of [(131073, 2), 262100, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6446, 262146, F64, 16) (dual of [262146, 262100, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6446, 262147, F64, 16) (dual of [262147, 262101, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(6446, 262147, F64, 16) (dual of [262147, 262101, 17]-code), using
- OOA 2-folding [i] based on linear OA(6446, 262146, F64, 16) (dual of [262146, 262100, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(6446, 131073, F64, 2, 16) (dual of [(131073, 2), 262100, 17]-NRT-code), using
(46−16, 46, large)-Net in Base 64 — Upper bound on s
There is no (30, 46, large)-net in base 64, because
- 14 times m-reduction [i] would yield (30, 32, large)-net in base 64, but