MinT - Best Known (62, 62+65, s)-Nets in Base 9

Best Known (62, 62+65, s)-Nets in Base 9

(62, 62+65, 138)-Net over F₉ — Constructive and digital

Digital (62, 127, 138)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 45, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (17, 82, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(62, 62+65, 218)-Net over F₉ — Digital

Digital (62, 127, 218)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+65, 9124)-Net in Base 9 — Upper bound on s

There is no (62, 127, 9125)-net in base 9, because

1 times m-reduction [i] would yield (62, 126, 9125)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 721107 639843 450646 066256 710412 721327 347217 810588 751907 630891 069204 726837 563277 250975 370415 934311 541499 374153 359133 272321 > 9¹²⁶ [i]