Best Known (111, 111+48, s)-Nets in Base 3
(111, 111+48, 204)-Net over F3 — Constructive and digital
Digital (111, 159, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 53, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
(111, 111+48, 357)-Net over F3 — Digital
Digital (111, 159, 357)-net over F3, using
(111, 111+48, 7076)-Net in Base 3 — Upper bound on s
There is no (111, 159, 7077)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7292 911245 477225 270807 557497 337610 353238 458465 537941 711362 470320 834145 082657 > 3159 [i]