Best Known (85−56, 85, s)-Nets in Base 16
(85−56, 85, 65)-Net over F16 — Constructive and digital
Digital (29, 85, 65)-net over F16, using
- t-expansion [i] based on digital (6, 85, 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
(85−56, 85, 120)-Net in Base 16 — Constructive
(29, 85, 120)-net in base 16, using
- 5 times m-reduction [i] based on (29, 90, 120)-net in base 16, using
- base change [i] based on digital (11, 72, 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, 72, 120)-net over F32, using
(85−56, 85, 161)-Net over F16 — Digital
Digital (29, 85, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
(85−56, 85, 3390)-Net in Base 16 — Upper bound on s
There is no (29, 85, 3391)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 241357 799025 564662 805514 091560 334293 762397 241621 101133 947783 421003 801797 502963 284588 725178 654501 082521 > 1685 [i]