MinT - Best Known (162, 162+59, s)-Nets in Base 3

Best Known (162, 162+59, s)-Nets in Base 3

(162, 162+59, 288)-Net over F₃ — Constructive and digital

Digital (162, 221, 288)-net over F₃, using

t-expansion [i] based on 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]

(162, 162+59, 719)-Net over F₃ — Digital

Digital (162, 221, 719)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+59, 24272)-Net in Base 3 — Upper bound on s

There is no (162, 221, 24273)-net in base 3, because

1 times m-reduction [i] would yield (162, 220, 24273)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 926 153920 877226 373205 384678 673012 687132 497572 048785 841381 493879 304553 552810 778443 008819 494695 074521 747507 > 3²²⁰ [i]