Best Known (219−102, 219, s)-Nets in Base 4
(219−102, 219, 130)-Net over F4 — Constructive and digital
Digital (117, 219, 130)-net over F4, using
- t-expansion [i] based on digital (105, 219, 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
(219−102, 219, 195)-Net over F4 — Digital
Digital (117, 219, 195)-net over F4, using
(219−102, 219, 2505)-Net in Base 4 — Upper bound on s
There is no (117, 219, 2506)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 718499 902808 801086 426534 638799 912168 962711 475977 868689 896736 237068 422283 911124 641980 602085 647944 655991 670413 461879 067918 230922 640624 > 4219 [i]