Best Known (171−44, 171, s)-Nets in Base 4
(171−44, 171, 531)-Net over F4 — Constructive and digital
Digital (127, 171, 531)-net over F4, using
- 9 times m-reduction [i] based on digital (127, 180, 531)-net over F4, using
- trace code for nets [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
- trace code for nets [i] based on digital (7, 60, 177)-net over F64, using
(171−44, 171, 576)-Net in Base 4 — Constructive
(127, 171, 576)-net in base 4, using
- 43 times duplication [i] based on (124, 168, 576)-net in base 4, using
- t-expansion [i] based on (123, 168, 576)-net in base 4, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 48, 192)-net over F128, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- t-expansion [i] based on (123, 168, 576)-net in base 4, using
(171−44, 171, 1416)-Net over F4 — Digital
Digital (127, 171, 1416)-net over F4, using
(171−44, 171, 144319)-Net in Base 4 — Upper bound on s
There is no (127, 171, 144320)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 959111 761597 719079 259181 316030 166271 559558 254415 652927 301678 651494 341358 531508 125958 363560 064422 582909 > 4171 [i]