MinT - Best Known (69, 126, s)-Nets in Base 3

Best Known (69, 126, s)-Nets in Base 3

(69, 126, 68)-Net over F₃ — Constructive and digital

Digital (69, 126, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 63, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(69, 126, 90)-Net over F₃ — Digital

Digital (69, 126, 90)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 126, 734)-Net in Base 3 — Upper bound on s

There is no (69, 126, 735)-net in base 3, because

1 times m-reduction [i] would yield (69, 125, 735)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 437449 714313 557853 994848 499882 991437 633491 224103 751839 750601 > 3¹²⁵ [i]