MinT - Best Known (210−55, 210, s)-Nets in Base 3

Best Known (210−55, 210, s)-Nets in Base 3

(210−55, 210, 288)-Net over F₃ — Constructive and digital

Digital (155, 210, 288)-net over F₃, using

6 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 72, 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]

(210−55, 210, 740)-Net over F₃ — Digital

Digital (155, 210, 740)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−55, 210, 26929)-Net in Base 3 — Upper bound on s

There is no (155, 210, 26930)-net in base 3, because

1 times m-reduction [i] would yield (155, 209, 26930)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5232 833839 469941 011457 424044 577448 323837 389951 163944 538517 750014 437083 675925 963321 667281 979737 750817 > 3²⁰⁹ [i]