Best Known (67−25, 67, s)-Nets in Base 64
(67−25, 67, 593)-Net over F64 — Constructive and digital
Digital (42, 67, 593)-net over F64, using
- 1 times m-reduction [i] based on digital (42, 68, 593)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 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 (28, 54, 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 (1, 14, 80)-net over F64, using
- (u, u+v)-construction [i] based on
(67−25, 67, 5461)-Net in Base 64 — Constructive
(42, 67, 5461)-net in base 64, using
- 641 times duplication [i] based on (41, 66, 5461)-net in base 64, using
- net defined by OOA [i] based on OOA(6466, 5461, S64, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6466, 65533, S64, 25), using
- discarding factors based on OA(6466, 65538, S64, 25), using
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- discarding factors based on OA(6466, 65538, S64, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6466, 65533, S64, 25), using
- net defined by OOA [i] based on OOA(6466, 5461, S64, 25, 25), using
(67−25, 67, 17162)-Net over F64 — Digital
Digital (42, 67, 17162)-net over F64, using
(67−25, 67, large)-Net in Base 64 — Upper bound on s
There is no (42, 67, large)-net in base 64, because
- 23 times m-reduction [i] would yield (42, 44, large)-net in base 64, but