Best Known (37, 37+16, s)-Nets in Base 64
(37, 37+16, 32771)-Net over F64 — Constructive and digital
Digital (37, 53, 32771)-net over F64, using
- 641 times duplication [i] based on digital (36, 52, 32771)-net over F64, using
- net defined by OOA [i] based on linear OOA(6452, 32771, F64, 16, 16) (dual of [(32771, 16), 524284, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6452, 262168, F64, 16) (dual of [262168, 262116, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6452, 262171, F64, 16) (dual of [262171, 262119, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [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(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(646, 27, F64, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(6452, 262171, F64, 16) (dual of [262171, 262119, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(6452, 262168, F64, 16) (dual of [262168, 262116, 17]-code), using
- net defined by OOA [i] based on linear OOA(6452, 32771, F64, 16, 16) (dual of [(32771, 16), 524284, 17]-NRT-code), using
(37, 37+16, 262175)-Net over F64 — Digital
Digital (37, 53, 262175)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6453, 262175, F64, 16) (dual of [262175, 262122, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(7) [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(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(647, 31, F64, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- construction X applied to Ce(15) ⊂ Ce(7) [i] based on
(37, 37+16, large)-Net in Base 64 — Upper bound on s
There is no (37, 53, large)-net in base 64, because
- 14 times m-reduction [i] would yield (37, 39, large)-net in base 64, but