Best Known (235−112, 235, s)-Nets in Base 4
(235−112, 235, 130)-Net over F4 — Constructive and digital
Digital (123, 235, 130)-net over F4, using
- t-expansion [i] based on digital (105, 235, 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
(235−112, 235, 193)-Net over F4 — Digital
Digital (123, 235, 193)-net over F4, using
(235−112, 235, 2386)-Net in Base 4 — Upper bound on s
There is no (123, 235, 2387)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3084 825950 223312 562580 378696 563352 729864 640951 208875 736280 017629 257478 052120 975085 188934 302155 203480 927263 412746 972175 457843 715253 344301 017960 > 4235 [i]