Best Known (117, 117+82, s)-Nets in Base 4
(117, 117+82, 130)-Net over F4 — Constructive and digital
Digital (117, 199, 130)-net over F4, using
- t-expansion [i] based on digital (105, 199, 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
(117, 117+82, 264)-Net over F4 — Digital
Digital (117, 199, 264)-net over F4, using
(117, 117+82, 4464)-Net in Base 4 — Upper bound on s
There is no (117, 199, 4465)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 651025 815661 130722 905680 695603 023836 841548 195135 936776 012569 253029 743752 354602 882916 062357 638704 797508 727806 612367 871400 > 4199 [i]