MinT - Best Known (62, 62+29, s)-Nets in Base 9

Best Known (62, 62+29, s)-Nets in Base 9

(62, 62+29, 740)-Net over F₉ — Constructive and digital

Digital (62, 91, 740)-net over F₉, using

1 times m-reduction [i] based on digital (62, 92, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 46, 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]

(62, 62+29, 1797)-Net over F₉ — Digital

Digital (62, 91, 1797)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+29, 1029865)-Net in Base 9 — Upper bound on s

There is no (62, 91, 1029866)-net in base 9, because

1 times m-reduction [i] would yield (62, 90, 1029866)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 178121 667162 893712 994687 338167 787552 863380 867565 100107 221918 790194 807884 129304 706465 > 9⁹⁰ [i]