Best Known (212−94, 212, s)-Nets in Base 4
(212−94, 212, 130)-Net over F4 — Constructive and digital
Digital (118, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(212−94, 212, 221)-Net over F4 — Digital
Digital (118, 212, 221)-net over F4, using
(212−94, 212, 3143)-Net in Base 4 — Upper bound on s
There is no (118, 212, 3144)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 860099 729748 088119 644714 425561 548880 278058 638510 661870 138347 936998 056344 436023 296822 777232 938582 647897 637800 013643 411807 280680 > 4212 [i]