Best Known (117, 117+108, s)-Nets in Base 4
(117, 117+108, 130)-Net over F4 — Constructive and digital
Digital (117, 225, 130)-net over F4, using
- t-expansion [i] based on digital (105, 225, 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
(117, 117+108, 181)-Net over F4 — Digital
Digital (117, 225, 181)-net over F4, using
(117, 117+108, 2210)-Net in Base 4 — Upper bound on s
There is no (117, 225, 2211)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2970 892323 290197 181385 507949 292961 188779 964506 026636 729244 066728 588856 313044 347078 931471 910231 660533 530823 355445 533500 844682 056161 827040 > 4225 [i]