Best Known (164, 164+90, s)-Nets in Base 4
(164, 164+90, 200)-Net over F4 — Constructive and digital
Digital (164, 254, 200)-net over F4, using
- t-expansion [i] based on digital (161, 254, 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+90, 240)-Net in Base 4 — Constructive
(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
(164, 164+90, 547)-Net over F4 — Digital
Digital (164, 254, 547)-net over F4, using
(164, 164+90, 14664)-Net in Base 4 — Upper bound on s
There is no (164, 254, 14665)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 840 496842 411135 013136 833577 345049 749137 957127 833772 981456 519826 047970 580557 311656 128340 754233 460593 739165 632546 049262 475698 577421 163076 936084 713321 365632 > 4254 [i]