Best Known (129, 193, s)-Nets in Base 4
(129, 193, 195)-Net over F4 — Constructive and digital
Digital (129, 193, 195)-net over F4, using
- 41 times duplication [i] based on digital (128, 192, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 64, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 64, 65)-net over F64, using
(129, 193, 240)-Net in Base 4 — Constructive
(129, 193, 240)-net in base 4, using
- 3 times m-reduction [i] based on (129, 196, 240)-net in base 4, using
- trace code for nets [i] based on (31, 98, 120)-net in base 16, using
- 2 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- base change [i] based on digital (11, 80, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 80, 120)-net over F32, using
- 2 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- trace code for nets [i] based on (31, 98, 120)-net in base 16, using
(129, 193, 543)-Net over F4 — Digital
Digital (129, 193, 543)-net over F4, using
(129, 193, 18210)-Net in Base 4 — Upper bound on s
There is no (129, 193, 18211)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 157 882198 881321 667567 342425 197996 947959 735620 337053 150753 261405 812298 968198 772758 415025 896068 262370 024565 325550 667225 > 4193 [i]