MinT - Best Known (161−41, 161, s)-Nets in Base 3

Best Known (161−41, 161, s)-Nets in Base 3

(161−41, 161, 288)-Net over F₃ — Constructive and digital

Digital (120, 161, 288)-net over F₃, using

t-expansion [i] based on digital (119, 161, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (119, 162, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 54, 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]

(161−41, 161, 665)-Net over F₃ — Digital

Digital (120, 161, 665)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−41, 161, 27222)-Net in Base 3 — Upper bound on s

There is no (120, 161, 27223)-net in base 3, because

1 times m-reduction [i] would yield (120, 160, 27223)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21848 047240 578370 269120 980884 251404 292910 679914 730089 577540 745158 121615 646041 > 3¹⁶⁰ [i]