MinT - Best Known (93−29, 93, s)-Nets in Base 9

Best Known (93−29, 93, s)-Nets in Base 9

(93−29, 93, 740)-Net over F₉ — Constructive and digital

Digital (64, 93, 740)-net over F₉, using

3 times m-reduction [i] based on digital (64, 96, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 48, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(93−29, 93, 2100)-Net over F₉ — Digital

Digital (64, 93, 2100)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−29, 93, 1409618)-Net in Base 9 — Upper bound on s

There is no (64, 93, 1409619)-net in base 9, because

1 times m-reduction [i] would yield (64, 92, 1409619)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6170 373864 382766 905372 761126 293225 038694 253429 971430 218516 729578 854240 675135 229551 832785 > 9⁹² [i]