Best Known (56, 87, s)-Nets in Base 64
(56, 87, 723)-Net over F64 — Constructive and digital
Digital (56, 87, 723)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (13, 28, 210)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (1, 16, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- digital (0, 5, 65)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (28, 59, 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
- digital (13, 28, 210)-net over F64, using
(56, 87, 4369)-Net in Base 64 — Constructive
(56, 87, 4369)-net in base 64, using
- 643 times duplication [i] based on (53, 84, 4369)-net in base 64, using
- base change [i] based on digital (32, 63, 4369)-net over F256, using
- 2562 times duplication [i] based on digital (30, 61, 4369)-net over F256, using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using
- net defined by OOA [i] based on linear OOA(25661, 4369, F256, 31, 31) (dual of [(4369, 31), 135378, 32]-NRT-code), using
- 2562 times duplication [i] based on digital (30, 61, 4369)-net over F256, using
- base change [i] based on digital (32, 63, 4369)-net over F256, using
(56, 87, 33080)-Net over F64 — Digital
Digital (56, 87, 33080)-net over F64, using
(56, 87, large)-Net in Base 64 — Upper bound on s
There is no (56, 87, large)-net in base 64, because
- 29 times m-reduction [i] would yield (56, 58, large)-net in base 64, but