Best Known (219−100, 219, s)-Nets in Base 4
(219−100, 219, 130)-Net over F4 — Constructive and digital
Digital (119, 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
(219−100, 219, 207)-Net over F4 — Digital
Digital (119, 219, 207)-net over F4, using
(219−100, 219, 2774)-Net in Base 4 — Upper bound on s
There is no (119, 219, 2775)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 714732 375617 620024 603153 874702 709772 069010 331396 491805 778332 169809 861779 924465 867618 086799 080787 116830 651331 971220 368189 630764 209906 > 4219 [i]