MinT - Best Known (221−60, 221, s)-Nets in Base 3

Best Known (221−60, 221, s)-Nets in Base 3

(221−60, 221, 288)-Net over F₃ — Constructive and digital

Digital (161, 221, 288)-net over F₃, using

4 times m-reduction [i] based on digital (161, 225, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 75, 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]

(221−60, 221, 677)-Net over F₃ — Digital

Digital (161, 221, 677)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−60, 221, 19674)-Net in Base 3 — Upper bound on s

There is no (161, 221, 19675)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2780 930756 275278 155055 417331 366252 015440 231158 644244 747652 828835 521801 073938 457244 973832 737230 186135 967645 > 3²²¹ [i]