Best Known (109, 109+38, s)-Nets in Base 4
(109, 109+38, 531)-Net over F4 — Constructive and digital
Digital (109, 147, 531)-net over F4, using
- 6 times m-reduction [i] based on digital (109, 153, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 51, 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, 51, 177)-net over F64, using
(109, 109+38, 576)-Net in Base 4 — Constructive
(109, 147, 576)-net in base 4, using
- t-expansion [i] based on (108, 147, 576)-net in base 4, using
- trace code for nets [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
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
(109, 109+38, 1223)-Net over F4 — Digital
Digital (109, 147, 1223)-net over F4, using
(109, 109+38, 120249)-Net in Base 4 — Upper bound on s
There is no (109, 147, 120250)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 31833 023788 329535 154641 837335 325897 059756 215922 976024 620995 619121 996546 851500 735441 916076 > 4147 [i]