Best Known (34, 34+16, s)-Nets in Base 64
(34, 34+16, 32770)-Net over F64 — Constructive and digital
Digital (34, 50, 32770)-net over F64, using
- net defined by OOA [i] based on linear OOA(6450, 32770, F64, 16, 16) (dual of [(32770, 16), 524270, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6450, 262160, F64, 16) (dual of [262160, 262110, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(6450, 262160, F64, 16) (dual of [262160, 262110, 17]-code), using
(34, 34+16, 201249)-Net over F64 — Digital
Digital (34, 50, 201249)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6450, 201249, F64, 16) (dual of [201249, 201199, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
(34, 34+16, large)-Net in Base 64 — Upper bound on s
There is no (34, 50, large)-net in base 64, because
- 14 times m-reduction [i] would yield (34, 36, large)-net in base 64, but