Best Known (84, 84+47, s)-Nets in Base 3
(84, 84+47, 148)-Net over F3 — Constructive and digital
Digital (84, 131, 148)-net over F3, using
- 3 times m-reduction [i] based on digital (84, 134, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 67, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 67, 74)-net over F9, using
(84, 84+47, 179)-Net over F3 — Digital
Digital (84, 131, 179)-net over F3, using
(84, 84+47, 2322)-Net in Base 3 — Upper bound on s
There is no (84, 131, 2323)-net in base 3, because
- 1 times m-reduction [i] would yield (84, 130, 2323)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 106 225326 186829 908263 673608 616673 525937 475296 748177 508217 030691 > 3130 [i]