MinT - Best Known (213−59, 213, s)-Nets in Base 3

Best Known (213−59, 213, s)-Nets in Base 3

(213−59, 213, 288)-Net over F₃ — Constructive and digital

Digital (154, 213, 288)-net over F₃, using

t-expansion [i] based on digital (153, 213, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 71, 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]

(213−59, 213, 611)-Net over F₃ — Digital

Digital (154, 213, 611)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−59, 213, 17919)-Net in Base 3 — Upper bound on s

There is no (154, 213, 17920)-net in base 3, because

1 times m-reduction [i] would yield (154, 212, 17920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141297 479566 318852 482341 948027 251369 718950 682056 124338 510485 944841 935351 667548 523645 475505 609723 669505 > 3²¹² [i]