MinT - Best Known (90, 90+45, s)-Nets in Base 3

Best Known (90, 90+45, s)-Nets in Base 3

(90, 90+45, 156)-Net over F₃ — Constructive and digital

Digital (90, 135, 156)-net over F₃, using

1 times m-reduction [i] based on digital (90, 136, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 68, 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]

(90, 90+45, 229)-Net over F₃ — Digital

Digital (90, 135, 229)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+45, 3625)-Net in Base 3 — Upper bound on s

There is no (90, 135, 3626)-net in base 3, because

1 times m-reduction [i] would yield (90, 134, 3626)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8622 863301 183125 772334 871860 532533 514615 711731 775046 729561 202509 > 3¹³⁴ [i]