MinT - Best Known (89−29, 89, s)-Nets in Base 3

Best Known (89−29, 89, s)-Nets in Base 3

(89−29, 89, 128)-Net over F₃ — Constructive and digital

Digital (60, 89, 128)-net over F₃, using

5 times m-reduction [i] based on digital (60, 94, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 47, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(89−29, 89, 177)-Net over F₃ — Digital

Digital (60, 89, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−29, 89, 3002)-Net in Base 3 — Upper bound on s

There is no (60, 89, 3003)-net in base 3, because

1 times m-reduction [i] would yield (60, 88, 3003)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 970526 254873 711526 821866 998016 272718 787581 > 3⁸⁸ [i]