MinT - Best Known (60, 60+37, s)-Nets in Base 3

Best Known (60, 60+37, s)-Nets in Base 3

(60, 60+37, 80)-Net over F₃ — Constructive and digital

Digital (60, 97, 80)-net over F₃, using

7 times m-reduction [i] based on digital (60, 104, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 52, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(60, 60+37, 118)-Net over F₃ — Digital

Digital (60, 97, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+37, 1306)-Net in Base 3 — Upper bound on s

There is no (60, 97, 1307)-net in base 3, because

1 times m-reduction [i] would yield (60, 96, 1307)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6435 272317 955706 497277 805846 713443 423514 011061 > 3⁹⁶ [i]