Best Known (35, 51, s)-Nets in Base 64
(35, 51, 32770)-Net over F64 — Constructive and digital
Digital (35, 51, 32770)-net over F64, using
- 641 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(6450, 32770, F64, 16, 16) (dual of [(32770, 16), 524270, 17]-NRT-code), using
(35, 51, 262167)-Net over F64 — Digital
Digital (35, 51, 262167)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6451, 262167, F64, 16) (dual of [262167, 262116, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [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(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
(35, 51, large)-Net in Base 64 — Upper bound on s
There is no (35, 51, large)-net in base 64, because
- 14 times m-reduction [i] would yield (35, 37, large)-net in base 64, but