Best Known (106, 106+67, s)-Nets in Base 4
(106, 106+67, 130)-Net over F4 — Constructive and digital
Digital (106, 173, 130)-net over F4, using
- t-expansion [i] based on digital (105, 173, 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
(106, 106+67, 287)-Net over F4 — Digital
Digital (106, 173, 287)-net over F4, using
(106, 106+67, 6002)-Net in Base 4 — Upper bound on s
There is no (106, 173, 6003)-net in base 4, because
- 1 times m-reduction [i] would yield (106, 172, 6003)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 36 031050 030154 392623 357517 471707 650604 812134 048693 645586 365615 484926 125301 646878 014081 795100 350368 465690 > 4172 [i]