MinT - Best Known (81, 116, s)-Nets in Base 3

Best Known (81, 116, s)-Nets in Base 3

(81, 116, 156)-Net over F₃ — Constructive and digital

Digital (81, 116, 156)-net over F₃, using

2 times m-reduction [i] based on digital (81, 118, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 59, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(81, 116, 278)-Net over F₃ — Digital

Digital (81, 116, 278)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 116, 6043)-Net in Base 3 — Upper bound on s

There is no (81, 116, 6044)-net in base 3, because

1 times m-reduction [i] would yield (81, 115, 6044)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 397113 360923 548831 188300 063653 607613 795990 671236 235065 > 3¹¹⁵ [i]