Best Known (212−104, 212, s)-Nets in Base 4
(212−104, 212, 130)-Net over F4 — Constructive and digital
Digital (108, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(212−104, 212, 161)-Net over F4 — Digital
Digital (108, 212, 161)-net over F4, using
(212−104, 212, 1877)-Net in Base 4 — Upper bound on s
There is no (108, 212, 1878)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 739492 632483 248279 405583 386272 224730 011835 695083 875094 421659 313594 040491 015290 867238 909815 107246 105214 937924 464966 577633 140898 > 4212 [i]