MinT - Best Known (54, 54+51, s)-Nets in Base 9

Best Known (54, 54+51, s)-Nets in Base 9

(54, 54+51, 200)-Net over F₉ — Constructive and digital

Digital (54, 105, 200)-net over F₉, using

1 times m-reduction [i] based on digital (54, 106, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 53, 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]

(54, 54+51, 233)-Net over F₉ — Digital

Digital (54, 105, 233)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+51, 11847)-Net in Base 9 — Upper bound on s

There is no (54, 105, 11848)-net in base 9, because

1 times m-reduction [i] would yield (54, 104, 11848)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1744 120156 202469 966116 310764 697452 207705 166379 313219 453390 648520 710935 138508 790171 167390 403789 165633 > 9¹⁰⁴ [i]