Best Known (232−102, 232, s)-Nets in Base 4
(232−102, 232, 130)-Net over F4 — Constructive and digital
Digital (130, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(232−102, 232, 246)-Net over F4 — Digital
Digital (130, 232, 246)-net over F4, using
(232−102, 232, 3584)-Net in Base 4 — Upper bound on s
There is no (130, 232, 3585)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47 679839 982749 573512 107931 300540 663281 031924 084712 070630 218019 729796 038929 459847 984066 788983 877874 938687 943981 223147 715040 903005 951887 352320 > 4232 [i]