Best Known (96−60, 96, s)-Nets in Base 16
(96−60, 96, 82)-Net over F16 — Constructive and digital
Digital (36, 96, 82)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 30, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (6, 66, 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 (0, 30, 17)-net over F16, using
(96−60, 96, 120)-Net in Base 16 — Constructive
(36, 96, 120)-net in base 16, using
- 29 times m-reduction [i] based on (36, 125, 120)-net in base 16, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
(96−60, 96, 193)-Net over F16 — Digital
Digital (36, 96, 193)-net over F16, using
- t-expansion [i] based on digital (33, 96, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(96−60, 96, 5709)-Net in Base 16 — Upper bound on s
There is no (36, 96, 5710)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 39 421078 198489 859837 050372 827419 508923 119632 625052 905656 678360 477783 369688 378240 045439 856175 354079 026087 861898 121376 > 1696 [i]