MinT - Best Known (62−29, 62, s)-Nets in Base 3

Best Known (62−29, 62, s)-Nets in Base 3

(62−29, 62, 40)-Net over F₃ — Constructive and digital

Digital (33, 62, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 31, 20)-net over F₉, using
- net from sequence [i] based on digital (2, 19)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [i]

(62−29, 62, 48)-Net over F₃ — Digital

Digital (33, 62, 48)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−29, 62, 349)-Net in Base 3 — Upper bound on s

There is no (33, 62, 350)-net in base 3, because

1 times m-reduction [i] would yield (33, 61, 350)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 131106 125292 468113 854598 056821 > 3⁶¹ [i]