Best Known (49−22, 49, s)-Nets in Base 64
(49−22, 49, 374)-Net over F64 — Constructive and digital
Digital (27, 49, 374)-net over F64, using
- net defined by OOA [i] based on linear OOA(6449, 374, F64, 22, 22) (dual of [(374, 22), 8179, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6449, 4114, F64, 22) (dual of [4114, 4065, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6449, 4116, F64, 22) (dual of [4116, 4067, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-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(21) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(6449, 4116, F64, 22) (dual of [4116, 4067, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6449, 4114, F64, 22) (dual of [4114, 4065, 23]-code), using
(49−22, 49, 517)-Net in Base 64 — Constructive
(27, 49, 517)-net in base 64, using
- 1 times m-reduction [i] based on (27, 50, 517)-net in base 64, using
- (u, u+v)-construction [i] based on
- (5, 16, 258)-net in base 64, using
- base change [i] based on digital (1, 12, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 12, 258)-net over F256, using
- (11, 34, 259)-net in base 64, using
- 2 times m-reduction [i] based on (11, 36, 259)-net in base 64, using
- base change [i] based on digital (2, 27, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 27, 259)-net over F256, using
- 2 times m-reduction [i] based on (11, 36, 259)-net in base 64, using
- (5, 16, 258)-net in base 64, using
- (u, u+v)-construction [i] based on
(49−22, 49, 2841)-Net over F64 — Digital
Digital (27, 49, 2841)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6449, 2841, F64, 22) (dual of [2841, 2792, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6449, 4116, F64, 22) (dual of [4116, 4067, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-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(21) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(6449, 4116, F64, 22) (dual of [4116, 4067, 23]-code), using
(49−22, 49, large)-Net in Base 64 — Upper bound on s
There is no (27, 49, large)-net in base 64, because
- 20 times m-reduction [i] would yield (27, 29, large)-net in base 64, but