Best Known (69, 69+30, s)-Nets in Base 3
(69, 69+30, 156)-Net over F3 — Constructive and digital
Digital (69, 99, 156)-net over F3, using
- trace code for nets [i] based on digital (3, 33, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
(69, 69+30, 243)-Net over F3 — Digital
Digital (69, 99, 243)-net over F3, using
(69, 69+30, 4511)-Net in Base 3 — Upper bound on s
There is no (69, 99, 4512)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 171933 394068 114300 259632 443804 203458 293436 955521 > 399 [i]