MinT - Best Known (61, 61+37, s)-Nets in Base 3

Best Known (61, 61+37, s)-Nets in Base 3

(61, 61+37, 80)-Net over F₃ — Constructive and digital

Digital (61, 98, 80)-net over F₃, using

8 times m-reduction [i] based on digital (61, 106, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 53, 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]

(61, 61+37, 123)-Net over F₃ — Digital

Digital (61, 98, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+37, 1389)-Net in Base 3 — Upper bound on s

There is no (61, 98, 1390)-net in base 3, because

1 times m-reduction [i] would yield (61, 97, 1390)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19220 628999 300907 300747 867331 847446 175477 920061 > 3⁹⁷ [i]