Best Known (106, 106+102, s)-Nets in Base 4
(106, 106+102, 130)-Net over F4 — Constructive and digital
Digital (106, 208, 130)-net over F4, using
- t-expansion [i] based on digital (105, 208, 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
(106, 106+102, 158)-Net over F4 — Digital
Digital (106, 208, 158)-net over F4, using
(106, 106+102, 1847)-Net in Base 4 — Upper bound on s
There is no (106, 208, 1848)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 172963 306924 945854 278952 396136 463046 593681 984472 541483 777018 679564 002169 840803 519509 182652 467255 948414 301516 136057 632860 800825 > 4208 [i]