Best Known (209−98, 209, s)-Nets in Base 4
(209−98, 209, 130)-Net over F4 — Constructive and digital
Digital (111, 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
(209−98, 209, 183)-Net over F4 — Digital
Digital (111, 209, 183)-net over F4, using
(209−98, 209, 2315)-Net in Base 4 — Upper bound on s
There is no (111, 209, 2316)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 679314 954672 281787 622521 681474 596589 980578 695615 096347 654966 923523 214003 716548 722162 672507 130720 618323 535213 872972 531008 326000 > 4209 [i]