Best Known (165, 165+90, s)-Nets in Base 4
(165, 165+90, 200)-Net over F4 — Constructive and digital
Digital (165, 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
(165, 165+90, 240)-Net in Base 4 — Constructive
(165, 255, 240)-net in base 4, using
- 1 times m-reduction [i] based on (165, 256, 240)-net in base 4, using
- trace code for nets [i] based on (37, 128, 120)-net in base 16, using
- 2 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
- 2 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- trace code for nets [i] based on (37, 128, 120)-net in base 16, using
(165, 165+90, 557)-Net over F4 — Digital
Digital (165, 255, 557)-net over F4, using
(165, 165+90, 15123)-Net in Base 4 — Upper bound on s
There is no (165, 255, 15124)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3352 379895 988504 902770 177403 258816 033732 142096 267079 927459 104872 811939 012924 616820 792464 069244 875121 453909 270355 674565 929122 498895 578971 718263 741277 844256 > 4255 [i]