Best Known (163, 163+92, s)-Nets in Base 4
(163, 163+92, 200)-Net over F4 — Constructive and digital
Digital (163, 255, 200)-net over F4, using
- t-expansion [i] based on digital (161, 255, 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
(163, 163+92, 208)-Net in Base 4 — Constructive
(163, 255, 208)-net in base 4, using
- 1 times m-reduction [i] based on (163, 256, 208)-net in base 4, using
- trace code for nets [i] based on (35, 128, 104)-net in base 16, using
- 2 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- 2 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- trace code for nets [i] based on (35, 128, 104)-net in base 16, using
(163, 163+92, 515)-Net over F4 — Digital
Digital (163, 255, 515)-net over F4, using
(163, 163+92, 13012)-Net in Base 4 — Upper bound on s
There is no (163, 255, 13013)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3359 719624 734770 912758 808608 361658 445414 997054 178935 777430 155660 971679 733427 780541 663870 794439 005803 161869 092024 627051 407217 186325 241819 767206 084494 502160 > 4255 [i]