MinT - Best Known (62, 62+51, s)-Nets in Base 3

Best Known (62, 62+51, s)-Nets in Base 3

(62, 62+51, 64)-Net over F₃ — Constructive and digital

Digital (62, 113, 64)-net over F₃, using

1 times m-reduction [i] based on digital (62, 114, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 57, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(62, 62+51, 83)-Net over F₃ — Digital

Digital (62, 113, 83)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+51, 674)-Net in Base 3 — Upper bound on s

There is no (62, 113, 675)-net in base 3, because

1 times m-reduction [i] would yield (62, 112, 675)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 281403 463134 254311 521362 445819 799050 570195 279803 101015 > 3¹¹² [i]