MinT - Best Known (216−55, 216, s)-Nets in Base 3

Best Known (216−55, 216, s)-Nets in Base 3

(216−55, 216, 288)-Net over F₃ — Constructive and digital

Digital (161, 216, 288)-net over F₃, using

9 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]

(216−55, 216, 843)-Net over F₃ — Digital

Digital (161, 216, 843)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−55, 216, 34382)-Net in Base 3 — Upper bound on s

There is no (161, 216, 34383)-net in base 3, because

1 times m-reduction [i] would yield (161, 215, 34383)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 811886 486913 134668 385191 604409 251222 946640 480306 490600 895286 533051 303881 242534 347362 781999 920430 808331 > 3²¹⁵ [i]