MinT - Best Known (64−27, 64, s)-Nets in Base 3

Best Known (64−27, 64, s)-Nets in Base 3

(64−27, 64, 64)-Net over F₃ — Constructive and digital

Digital (37, 64, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 32, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(64−27, 64, 65)-Net over F₃ — Digital

Digital (37, 64, 65)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−27, 64, 569)-Net in Base 3 — Upper bound on s

There is no (37, 64, 570)-net in base 3, because

1 times m-reduction [i] would yield (37, 63, 570)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 166483 388029 743801 844861 554557 > 3⁶³ [i]