Best Known (164, 164+88, s)-Nets in Base 4
(164, 164+88, 200)-Net over F4 — Constructive and digital
Digital (164, 252, 200)-net over F4, using
- t-expansion [i] based on digital (161, 252, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(164, 164+88, 240)-Net in Base 4 — Constructive
(164, 252, 240)-net in base 4, using
- 2 times m-reduction [i] based on (164, 254, 240)-net in base 4, using
- trace code for nets [i] based on (37, 127, 120)-net in base 16, using
- 3 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 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, 104, 120)-net over F32, using
- 3 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- trace code for nets [i] based on (37, 127, 120)-net in base 16, using
(164, 164+88, 572)-Net over F4 — Digital
Digital (164, 252, 572)-net over F4, using
(164, 164+88, 16106)-Net in Base 4 — Upper bound on s
There is no (164, 252, 16107)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 52 505319 821025 442534 251028 694192 374972 990114 480613 448767 324513 152023 243686 510016 124797 802828 557822 639805 351571 762872 031060 181814 758915 982187 407622 913232 > 4252 [i]