MinT - Best Known (215−99, 215, s)-Nets in Base 3

Best Known (215−99, 215, s)-Nets in Base 3

(215−99, 215, 80)-Net over F₃ — Constructive and digital

Digital (116, 215, 80)-net over F₃, using

1 times m-reduction [i] based on digital (116, 216, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 108, 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]

(215−99, 215, 134)-Net over F₃ — Digital

Digital (116, 215, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−99, 215, 1111)-Net in Base 3 — Upper bound on s

There is no (116, 215, 1112)-net in base 3, because

1 times m-reduction [i] would yield (116, 214, 1112)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 314636 420909 307937 968065 076404 669511 409408 765343 969145 765375 094401 594141 779922 317727 303893 127410 806193 > 3²¹⁴ [i]