MinT - Best Known (65, 65+31, s)-Nets in Base 3

Best Known (65, 65+31, s)-Nets in Base 3

(65, 65+31, 148)-Net over F₃ — Constructive and digital

Digital (65, 96, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 48, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(65, 65+31, 192)-Net over F₃ — Digital

Digital (65, 96, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+31, 3362)-Net in Base 3 — Upper bound on s

There is no (65, 96, 3363)-net in base 3, because

1 times m-reduction [i] would yield (65, 95, 3363)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2127 308632 252001 133709 584952 105416 504211 103091 > 3⁹⁵ [i]