Best Known (221−84, 221, s)-Nets in Base 4
(221−84, 221, 138)-Net over F4 — Constructive and digital
Digital (137, 221, 138)-net over F4, using
- 2 times m-reduction [i] based on digital (137, 223, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 64, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- digital (73, 159, 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 (21, 64, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(221−84, 221, 379)-Net over F4 — Digital
Digital (137, 221, 379)-net over F4, using
(221−84, 221, 8068)-Net in Base 4 — Upper bound on s
There is no (137, 221, 8069)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11 364198 327460 047394 064276 949556 617304 544373 305221 702032 225165 916858 819749 226916 406277 288717 694966 384976 741833 691919 059059 890050 383200 > 4221 [i]