MinT - Best Known (123−49, 123, s)-Nets in Base 9

Best Known (123−49, 123, s)-Nets in Base 9

(123−49, 123, 344)-Net over F₉ — Constructive and digital

Digital (74, 123, 344)-net over F₉, using

11 times m-reduction [i] based on digital (74, 134, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 67, 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]

(123−49, 123, 664)-Net over F₉ — Digital

Digital (74, 123, 664)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−49, 123, 86882)-Net in Base 9 — Upper bound on s

There is no (74, 123, 86883)-net in base 9, because

1 times m-reduction [i] would yield (74, 122, 86883)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 594556 989159 879232 731782 159698 117254 078436 026708 761866 109005 331403 791542 138312 303408 293450 469541 790569 163503 908929 > 9¹²² [i]