Best Known (107, 107+38, s)-Nets in Base 4
(107, 107+38, 531)-Net over F4 — Constructive and digital
Digital (107, 145, 531)-net over F4, using
- 5 times m-reduction [i] based on digital (107, 150, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 50, 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, 50, 177)-net over F64, using
(107, 107+38, 576)-Net in Base 4 — Constructive
(107, 145, 576)-net in base 4, using
- 41 times duplication [i] based on (106, 144, 576)-net in base 4, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
- 1 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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, 42, 192)-net over F128, using
- 1 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
(107, 107+38, 1136)-Net over F4 — Digital
Digital (107, 145, 1136)-net over F4, using
(107, 107+38, 103919)-Net in Base 4 — Upper bound on s
There is no (107, 145, 103920)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1989 345428 560093 409287 494047 294489 883181 871938 042185 096112 302118 341666 271609 324056 882262 > 4145 [i]