Best Known (222−143, 222, s)-Nets in Base 4
(222−143, 222, 104)-Net over F4 — Constructive and digital
Digital (79, 222, 104)-net over F4, using
- t-expansion [i] based on digital (73, 222, 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
(222−143, 222, 112)-Net over F4 — Digital
Digital (79, 222, 112)-net over F4, using
- t-expansion [i] based on digital (73, 222, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(222−143, 222, 623)-Net in Base 4 — Upper bound on s
There is no (79, 222, 624)-net in base 4, because
- 1 times m-reduction [i] would yield (79, 221, 624)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 338330 827235 260973 998259 835068 344957 744586 710712 759936 263823 648487 149272 309139 508698 463903 758341 025394 998563 058733 501922 432197 738763 > 4221 [i]