MinT - Best Known (61, 61+51, s)-Nets in Base 3

Best Known (61, 61+51, s)-Nets in Base 3

(61, 61+51, 64)-Net over F₃ — Constructive and digital

Digital (61, 112, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 56, 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]

(61, 61+51, 80)-Net over F₃ — Digital

Digital (61, 112, 80)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+51, 644)-Net in Base 3 — Upper bound on s

There is no (61, 112, 645)-net in base 3, because

1 times m-reduction [i] would yield (61, 111, 645)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 93951 694621 592918 533730 666626 424290 564612 317314 992683 > 3¹¹¹ [i]