MinT - Best Known (207−93, 207, s)-Nets in Base 3

Best Known (207−93, 207, s)-Nets in Base 3

(207−93, 207, 80)-Net over F₃ — Constructive and digital

Digital (114, 207, 80)-net over F₃, using

5 times m-reduction [i] based on digital (114, 212, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 106, 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]

(207−93, 207, 139)-Net over F₃ — Digital

Digital (114, 207, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−93, 207, 1187)-Net in Base 3 — Upper bound on s

There is no (114, 207, 1188)-net in base 3, because

1 times m-reduction [i] would yield (114, 206, 1188)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194 127329 367840 082987 738136 176433 723612 457994 865849 502133 501404 426371 031738 367150 748289 352083 584921 > 3²⁰⁶ [i]