MinT - Best Known (83, 83+69, s)-Nets in Base 3

Best Known (83, 83+69, s)-Nets in Base 3

(83, 83+69, 72)-Net over F₃ — Constructive and digital

Digital (83, 152, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 76, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(83, 83+69, 104)-Net over F₃ — Digital

Digital (83, 152, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+69, 857)-Net in Base 3 — Upper bound on s

There is no (83, 152, 858)-net in base 3, because

1 times m-reduction [i] would yield (83, 151, 858)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 149325 518047 915526 098643 047245 813634 185526 775705 036903 855411 173938 160805 > 3¹⁵¹ [i]