Best Known (171−76, 171, s)-Nets in Base 4
(171−76, 171, 130)-Net over F4 — Constructive and digital
Digital (95, 171, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (95, 178, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 89, 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
- trace code for nets [i] based on digital (6, 89, 65)-net over F16, using
(171−76, 171, 182)-Net over F4 — Digital
Digital (95, 171, 182)-net over F4, using
(171−76, 171, 2533)-Net in Base 4 — Upper bound on s
There is no (95, 171, 2534)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 068826 304044 187521 908237 813693 025425 080463 208102 000769 303491 154724 680537 937224 374327 960775 895385 912520 > 4171 [i]