Best Known (140, 235, s)-Nets in Base 4
(140, 235, 137)-Net over F4 — Constructive and digital
Digital (140, 235, 137)-net over F4, using
- 9 times m-reduction [i] based on digital (140, 244, 137)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 67, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (73, 177, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (15, 67, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(140, 235, 326)-Net over F4 — Digital
Digital (140, 235, 326)-net over F4, using
(140, 235, 6049)-Net in Base 4 — Upper bound on s
There is no (140, 235, 6050)-net in base 4, because
- 1 times m-reduction [i] would yield (140, 234, 6050)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 766 056211 288211 960430 028106 699704 997999 545837 291229 386923 038159 690668 296012 027244 224924 756710 261753 995160 753839 868054 799955 340889 369689 079232 > 4234 [i]