Best Known (217−94, 217, s)-Nets in Base 4
(217−94, 217, 130)-Net over F4 — Constructive and digital
Digital (123, 217, 130)-net over F4, using
- t-expansion [i] based on digital (105, 217, 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
(217−94, 217, 243)-Net over F4 — Digital
Digital (123, 217, 243)-net over F4, using
(217−94, 217, 3648)-Net in Base 4 — Upper bound on s
There is no (123, 217, 3649)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 44514 846794 064588 135823 120625 662856 608200 217478 845854 791141 582592 827705 322748 335306 933841 452018 896556 630805 965246 019335 614212 287040 > 4217 [i]