Best Known (122, 122+124, s)-Nets in Base 4
(122, 122+124, 130)-Net over F4 — Constructive and digital
Digital (122, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 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
(122, 122+124, 168)-Net over F4 — Digital
Digital (122, 246, 168)-net over F4, using
- t-expansion [i] based on digital (115, 246, 168)-net over F4, using
- net from sequence [i] based on digital (115, 167)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 115 and N(F) ≥ 168, using
- net from sequence [i] based on digital (115, 167)-sequence over F4, using
(122, 122+124, 1902)-Net in Base 4 — Upper bound on s
There is no (122, 246, 1903)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13070 179595 650771 895344 610015 309230 142839 112977 464610 116103 936819 610533 745596 394114 069390 344427 354112 873747 145178 073369 174248 181958 149294 138949 328740 > 4246 [i]