MinT - Best Known (64, 97, s)-Nets in Base 3

Best Known (64, 97, s)-Nets in Base 3

(64, 97, 128)-Net over F₃ — Constructive and digital

Digital (64, 97, 128)-net over F₃, using

5 times m-reduction [i] based on digital (64, 102, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 51, 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]

(64, 97, 165)-Net over F₃ — Digital

Digital (64, 97, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 97, 2463)-Net in Base 3 — Upper bound on s

There is no (64, 97, 2464)-net in base 3, because

1 times m-reduction [i] would yield (64, 96, 2464)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6391 058385 074657 164047 358420 630447 771549 595649 > 3⁹⁶ [i]