Best Known (209−92, 209, s)-Nets in Base 4
(209−92, 209, 130)-Net over F4 — Constructive and digital
Digital (117, 209, 130)-net over F4, using
- t-expansion [i] based on digital (105, 209, 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
(209−92, 209, 223)-Net over F4 — Digital
Digital (117, 209, 223)-net over F4, using
(209−92, 209, 3224)-Net in Base 4 — Upper bound on s
There is no (117, 209, 3225)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 678188 992845 649171 800272 840235 676539 873120 369830 113729 402850 107584 015251 481719 137988 081693 478193 574750 440510 563475 631608 844128 > 4209 [i]