Best Known (225−102, 225, s)-Nets in Base 4
(225−102, 225, 130)-Net over F4 — Constructive and digital
Digital (123, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(225−102, 225, 217)-Net over F4 — Digital
Digital (123, 225, 217)-net over F4, using
(225−102, 225, 2956)-Net in Base 4 — Upper bound on s
There is no (123, 225, 2957)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2928 793331 497072 103022 143869 967796 635551 263713 191620 464255 487679 542319 713239 707992 146795 488105 870973 820958 030019 079750 630200 273140 735840 > 4225 [i]