Best Known (138, 138+94, s)-Nets in Base 4
(138, 138+94, 137)-Net over F4 — Constructive and digital
Digital (138, 232, 137)-net over F4, using
- 6 times m-reduction [i] based on digital (138, 238, 137)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 65, 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, 173, 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, 65, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(138, 138+94, 320)-Net over F4 — Digital
Digital (138, 232, 320)-net over F4, using
(138, 138+94, 5700)-Net in Base 4 — Upper bound on s
There is no (138, 232, 5701)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47 791599 676185 211616 167169 507814 346334 773623 864810 484281 891928 518957 728560 013571 640926 600312 570282 819846 635206 353693 513033 657083 916697 085248 > 4232 [i]