Best Known (38, 38+34, s)-Nets in Base 64
(38, 38+34, 513)-Net over F64 — Constructive and digital
Digital (38, 72, 513)-net over F64, using
- t-expansion [i] based on digital (28, 72, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(38, 38+34, 517)-Net in Base 64 — Constructive
(38, 72, 517)-net in base 64, using
- base change [i] based on digital (20, 54, 517)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (2, 36, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (1, 18, 258)-net over F256, using
- (u, u+v)-construction [i] based on
(38, 38+34, 2056)-Net over F64 — Digital
Digital (38, 72, 2056)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6472, 2056, F64, 2, 34) (dual of [(2056, 2), 4040, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6472, 4112, F64, 34) (dual of [4112, 4040, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(6472, 4113, F64, 34) (dual of [4113, 4041, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(27) [i] based on
- linear OA(6467, 4096, F64, 34) (dual of [4096, 4029, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(6455, 4096, F64, 28) (dual of [4096, 4041, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-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(33) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(6472, 4113, F64, 34) (dual of [4113, 4041, 35]-code), using
- OOA 2-folding [i] based on linear OA(6472, 4112, F64, 34) (dual of [4112, 4040, 35]-code), using
(38, 38+34, 5085192)-Net in Base 64 — Upper bound on s
There is no (38, 72, 5085193)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 11090 709261 741446 877987 320395 248027 114122 341952 307130 102545 811220 698990 512758 713584 593670 535917 227125 253417 743520 441216 341777 079296 > 6472 [i]