MinT - Best Known (210−58, 210, s)-Nets in Base 3

Best Known (210−58, 210, s)-Nets in Base 3

(210−58, 210, 288)-Net over F₃ — Constructive and digital

Digital (152, 210, 288)-net over F₃, using

t-expansion [i] based on digital (151, 210, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 70, 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]

(210−58, 210, 610)-Net over F₃ — Digital

Digital (152, 210, 610)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−58, 210, 16609)-Net in Base 3 — Upper bound on s

There is no (152, 210, 16610)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15690 131525 905611 294765 875309 236170 607993 128990 412535 733115 476919 522528 100497 127820 672388 482520 877421 > 3²¹⁰ [i]