MinT - Best Known (229−62, 229, s)-Nets in Base 3

Best Known (229−62, 229, s)-Nets in Base 3

(229−62, 229, 288)-Net over F₃ — Constructive and digital

Digital (167, 229, 288)-net over F₃, using

5 times m-reduction [i] based on digital (167, 234, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 78, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(229−62, 229, 705)-Net over F₃ — Digital

Digital (167, 229, 705)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−62, 229, 20744)-Net in Base 3 — Upper bound on s

There is no (167, 229, 20745)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 238621 288704 668433 167271 804723 320013 753945 889545 783797 675089 680026 935609 718217 258390 987205 007280 618187 183179 > 3²²⁹ [i]