MinT - Best Known (137−44, 137, s)-Nets in Base 3

Best Known (137−44, 137, s)-Nets in Base 3

(137−44, 137, 156)-Net over F₃ — Constructive and digital

Digital (93, 137, 156)-net over F₃, using

5 times m-reduction [i] based on digital (93, 142, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 71, 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]

(137−44, 137, 260)-Net over F₃ — Digital

Digital (93, 137, 260)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−44, 137, 4214)-Net in Base 3 — Upper bound on s

There is no (93, 137, 4215)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 232246 561960 107566 859231 822127 906523 799146 864447 300883 758833 249029 > 3¹³⁷ [i]