Best Known (27, 27+16, s)-Nets in Base 64
(27, 27+16, 642)-Net over F64 — Constructive and digital
Digital (27, 43, 642)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 130)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (0, 4, 65)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (15, 31, 512)-net over F64, using
- net defined by OOA [i] based on linear OOA(6431, 512, F64, 16, 16) (dual of [(512, 16), 8161, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using
- net defined by OOA [i] based on linear OOA(6431, 512, F64, 16, 16) (dual of [(512, 16), 8161, 17]-NRT-code), using
- digital (4, 12, 130)-net over F64, using
(27, 27+16, 8192)-Net in Base 64 — Constructive
(27, 43, 8192)-net in base 64, using
- 1 times m-reduction [i] based on (27, 44, 8192)-net in base 64, using
- base change [i] based on digital (16, 33, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- base change [i] based on digital (16, 33, 8192)-net over F256, using
(27, 27+16, 15359)-Net over F64 — Digital
Digital (27, 43, 15359)-net over F64, using
(27, 27+16, large)-Net in Base 64 — Upper bound on s
There is no (27, 43, large)-net in base 64, because
- 14 times m-reduction [i] would yield (27, 29, large)-net in base 64, but