Best Known (33−15, 33, s)-Nets in Base 64
(33−15, 33, 587)-Net over F64 — Constructive and digital
Digital (18, 33, 587)-net over F64, using
- net defined by OOA [i] based on linear OOA(6433, 587, F64, 15, 15) (dual of [(587, 15), 8772, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-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(14) ⊂ Ce(9) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
(33−15, 33, 2507)-Net over F64 — Digital
Digital (18, 33, 2507)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6433, 2507, F64, 15) (dual of [2507, 2474, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-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(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(6433, 4110, F64, 15) (dual of [4110, 4077, 16]-code), using
(33−15, 33, large)-Net in Base 64 — Upper bound on s
There is no (18, 33, large)-net in base 64, because
- 13 times m-reduction [i] would yield (18, 20, large)-net in base 64, but