Best Known (112, 112+106, s)-Nets in Base 4
(112, 112+106, 130)-Net over F4 — Constructive and digital
Digital (112, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 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
(112, 112+106, 169)-Net over F4 — Digital
Digital (112, 218, 169)-net over F4, using
(112, 112+106, 2012)-Net in Base 4 — Upper bound on s
There is no (112, 218, 2013)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 177936 086131 781929 486602 162722 665369 012103 559178 166244 309633 123331 710057 161392 773259 899690 233178 773213 318849 561098 847733 207334 501960 > 4218 [i]