MinT - Best Known (62, 62+59, s)-Nets in Base 9

Best Known (62, 62+59, s)-Nets in Base 9

(62, 62+59, 200)-Net over F₉ — Constructive and digital

Digital (62, 121, 200)-net over F₉, using

1 times m-reduction [i] based on digital (62, 122, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 61, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(62, 62+59, 258)-Net over F₉ — Digital

Digital (62, 121, 258)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+59, 12942)-Net in Base 9 — Upper bound on s

There is no (62, 121, 12943)-net in base 9, because

1 times m-reduction [i] would yield (62, 120, 12943)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 230102 521176 965306 015684 772429 837259 136001 933451 351561 130913 410748 106894 406379 891726 934806 604890 217205 272102 839705 > 9¹²⁰ [i]