Best Known (66−36, 66, s)-Nets in Base 16
(66−36, 66, 130)-Net over F16 — Constructive and digital
Digital (30, 66, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 24, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (6, 42, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 24, 65)-net over F16, using
(66−36, 66, 168)-Net over F16 — Digital
Digital (30, 66, 168)-net over F16, using
(66−36, 66, 177)-Net in Base 16 — Constructive
(30, 66, 177)-net in base 16, using
- 3 times m-reduction [i] based on (30, 69, 177)-net in base 16, using
- base change [i] based on digital (7, 46, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 46, 177)-net over F64, using
(66−36, 66, 13086)-Net in Base 16 — Upper bound on s
There is no (30, 66, 13087)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 29 662951 643782 205840 595277 660464 952706 111825 253414 461040 610994 564449 894333 199641 > 1666 [i]