MinT - Best Known (138−62, 138, s)-Nets in Base 9

Best Known (138−62, 138, s)-Nets in Base 9

(138−62, 138, 344)-Net over F₉ — Constructive and digital

Digital (76, 138, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 69, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(138−62, 138, 410)-Net over F₉ — Digital

Digital (76, 138, 410)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−62, 138, 27451)-Net in Base 9 — Upper bound on s

There is no (76, 138, 27452)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485079 837738 998389 066365 785571 411142 345027 139782 621736 258349 042037 515364 062485 728919 041252 068373 490405 853028 493184 647302 458055 383969 > 9¹³⁸ [i]