MinT - Best Known (124−45, 124, s)-Nets in Base 3

Best Known (124−45, 124, s)-Nets in Base 3

(124−45, 124, 148)-Net over F₃ — Constructive and digital

Digital (79, 124, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 62, 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]

(124−45, 124, 166)-Net over F₃ — Digital

Digital (79, 124, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−45, 124, 2084)-Net in Base 3 — Upper bound on s

There is no (79, 124, 2085)-net in base 3, because

1 times m-reduction [i] would yield (79, 123, 2085)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48958 876759 677102 146854 433966 703270 314787 703518 802996 788417 > 3¹²³ [i]