Best Known (132, 132+66, s)-Nets in Base 4
(132, 132+66, 195)-Net over F4 — Constructive and digital
Digital (132, 198, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 66, 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
(132, 132+66, 240)-Net in Base 4 — Constructive
(132, 198, 240)-net in base 4, using
- t-expansion [i] based on (131, 198, 240)-net in base 4, using
- 2 times m-reduction [i] based on (131, 200, 240)-net in base 4, using
- trace code for nets [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
- trace code for nets [i] based on (31, 100, 120)-net in base 16, using
- 2 times m-reduction [i] based on (131, 200, 240)-net in base 4, using
(132, 132+66, 545)-Net over F4 — Digital
Digital (132, 198, 545)-net over F4, using
(132, 132+66, 17944)-Net in Base 4 — Upper bound on s
There is no (132, 198, 17945)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 161430 217562 680170 827702 168588 910264 163722 129376 796122 708504 919989 757569 949845 541941 544396 634835 808449 511835 185976 669760 > 4198 [i]