MinT - Best Known (162, 162+61, s)-Nets in Base 3

Best Known (162, 162+61, s)-Nets in Base 3

(162, 162+61, 288)-Net over F₃ — Constructive and digital

Digital (162, 223, 288)-net over F₃, using

t-expansion [i] based on digital (161, 223, 288)-net over F₃, using
- 2 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+61, 664)-Net over F₃ — Digital

Digital (162, 223, 664)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+61, 20409)-Net in Base 3 — Upper bound on s

There is no (162, 223, 20410)-net in base 3, because

1 times m-reduction [i] would yield (162, 222, 20410)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8343 273727 727335 494583 671539 239716 450898 571572 910808 109819 659702 573358 228443 607052 624661 414788 247612 610045 > 3²²² [i]