Best Known (195−65, 195, s)-Nets in Base 4
(195−65, 195, 195)-Net over F4 — Constructive and digital
Digital (130, 195, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 65, 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
(195−65, 195, 240)-Net in Base 4 — Constructive
(130, 195, 240)-net in base 4, using
- 3 times m-reduction [i] based on (130, 198, 240)-net in base 4, using
- trace code for nets [i] based on (31, 99, 120)-net in base 16, using
- 1 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
- 1 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
- trace code for nets [i] based on (31, 99, 120)-net in base 16, using
(195−65, 195, 538)-Net over F4 — Digital
Digital (130, 195, 538)-net over F4, using
(195−65, 195, 19017)-Net in Base 4 — Upper bound on s
There is no (130, 195, 19018)-net in base 4, because
- 1 times m-reduction [i] would yield (130, 194, 19018)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 631 075740 499724 950677 926431 194645 576462 873866 682139 583338 244586 352735 119798 217488 873336 268318 154151 994443 147223 447966 > 4194 [i]