MinT - Best Known (210−53, 210, s)-Nets in Base 3

Best Known (210−53, 210, s)-Nets in Base 3

(210−53, 210, 288)-Net over F₃ — Constructive and digital

Digital (157, 210, 288)-net over F₃, using

9 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 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]

(210−53, 210, 852)-Net over F₃ — Digital

Digital (157, 210, 852)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−53, 210, 36080)-Net in Base 3 — Upper bound on s

There is no (157, 210, 36081)-net in base 3, because

1 times m-reduction [i] would yield (157, 209, 36081)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5228 519076 041638 763930 915650 403599 288660 294437 953266 289103 086006 162886 837056 324973 928306 383095 135817 > 3²⁰⁹ [i]