Best Known (109, 171, s)-Nets in Base 4
(109, 171, 145)-Net over F4 — Constructive and digital
Digital (109, 171, 145)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 35, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- digital (74, 136, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 68, 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, 68, 65)-net over F16, using
- digital (4, 35, 15)-net over F4, using
(109, 171, 152)-Net in Base 4 — Constructive
(109, 171, 152)-net in base 4, using
- 41 times duplication [i] based on (108, 170, 152)-net in base 4, using
- t-expansion [i] based on (107, 170, 152)-net in base 4, using
- trace code for nets [i] based on (22, 85, 76)-net in base 16, using
- base change [i] based on digital (5, 68, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 68, 76)-net over F32, using
- trace code for nets [i] based on (22, 85, 76)-net in base 16, using
- t-expansion [i] based on (107, 170, 152)-net in base 4, using
(109, 171, 357)-Net over F4 — Digital
Digital (109, 171, 357)-net over F4, using
(109, 171, 8643)-Net in Base 4 — Upper bound on s
There is no (109, 171, 8644)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 979450 583084 839242 302440 520734 487047 146242 299343 040656 276633 113790 504685 721978 672161 106078 905167 623856 > 4171 [i]