MinT - Best Known (90−38, 90, s)-Nets in Base 9

Best Known (90−38, 90, s)-Nets in Base 9

(90−38, 90, 344)-Net over F₉ — Constructive and digital

Digital (52, 90, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 45, 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]

(90−38, 90, 390)-Net over F₉ — Digital

Digital (52, 90, 390)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−38, 90, 32814)-Net in Base 9 — Upper bound on s

There is no (52, 90, 32815)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 181660 638136 728694 101724 095441 082671 341435 907719 239520 800555 431545 732688 514522 474985 > 9⁹⁰ [i]