Best Known (85−48, 85, s)-Nets in Base 16
(85−48, 85, 130)-Net over F16 — Constructive and digital
Digital (37, 85, 130)-net over F16, using
- 2 times m-reduction [i] based on digital (37, 87, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 31, 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, 56, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 31, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(85−48, 85, 177)-Net in Base 16 — Constructive
(37, 85, 177)-net in base 16, using
- 5 times m-reduction [i] based on (37, 90, 177)-net in base 16, using
- base change [i] based on digital (7, 60, 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, 60, 177)-net over F64, using
(85−48, 85, 208)-Net over F16 — Digital
Digital (37, 85, 208)-net over F16, using
- net from sequence [i] based on digital (37, 207)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 37 and N(F) ≥ 208, using
(85−48, 85, 12005)-Net in Base 16 — Upper bound on s
There is no (37, 85, 12006)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 240826 174951 862144 819391 365265 713750 664520 498125 346643 893289 073630 236254 562849 732368 625790 293028 806636 > 1685 [i]