Best Known (87, 87+84, s)-Nets in Base 4
(87, 87+84, 104)-Net over F4 — Constructive and digital
Digital (87, 171, 104)-net over F4, using
- t-expansion [i] based on digital (73, 171, 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
(87, 87+84, 133)-Net over F4 — Digital
Digital (87, 171, 133)-net over F4, using
(87, 87+84, 1521)-Net in Base 4 — Upper bound on s
There is no (87, 171, 1522)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 084121 356345 966145 315725 432697 222690 039938 181600 784024 360742 193773 505875 044140 340082 847103 267562 928840 > 4171 [i]