Best Known (119, 119+42, s)-Nets in Base 4
(119, 119+42, 531)-Net over F4 — Constructive and digital
Digital (119, 161, 531)-net over F4, using
- 7 times m-reduction [i] based on digital (119, 168, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 56, 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, 56, 177)-net over F64, using
(119, 119+42, 576)-Net in Base 4 — Constructive
(119, 161, 576)-net in base 4, using
- 1 times m-reduction [i] based on (119, 162, 576)-net in base 4, using
- trace code for nets [i] based on (11, 54, 192)-net in base 64, using
- 2 times m-reduction [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
- 2 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 54, 192)-net in base 64, using
(119, 119+42, 1265)-Net over F4 — Digital
Digital (119, 161, 1265)-net over F4, using
(119, 119+42, 119427)-Net in Base 4 — Upper bound on s
There is no (119, 161, 119428)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 545349 632307 118224 783389 184125 764751 677816 776629 362194 832686 032660 690267 315841 057967 495329 863840 > 4161 [i]