Best Known (42, 42+26, s)-Nets in Base 64
(42, 42+26, 593)-Net over F64 — Constructive and digital
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
(42, 42+26, 5041)-Net in Base 64 — Constructive
(42, 68, 5041)-net in base 64, using
- base change [i] based on digital (25, 51, 5041)-net over F256, using
- net defined by OOA [i] based on linear OOA(25651, 5041, F256, 26, 26) (dual of [(5041, 26), 131015, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(25651, 65533, F256, 26) (dual of [65533, 65482, 27]-code), using
- net defined by OOA [i] based on linear OOA(25651, 5041, F256, 26, 26) (dual of [(5041, 26), 131015, 27]-NRT-code), using
(42, 42+26, 13228)-Net over F64 — Digital
Digital (42, 68, 13228)-net over F64, using
(42, 42+26, large)-Net in Base 64 — Upper bound on s
There is no (42, 68, large)-net in base 64, because
- 24 times m-reduction [i] would yield (42, 44, large)-net in base 64, but