MinT - Best Known (52, 52+49, s)-Nets in Base 9

Best Known (52, 52+49, s)-Nets in Base 9

(52, 52+49, 200)-Net over F₉ — Constructive and digital

Digital (52, 101, 200)-net over F₉, using

1 times m-reduction [i] based on digital (52, 102, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 51, 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]

(52, 52+49, 226)-Net over F₉ — Digital

Digital (52, 101, 226)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+49, 11580)-Net in Base 9 — Upper bound on s

There is no (52, 101, 11581)-net in base 9, because

1 times m-reduction [i] would yield (52, 100, 11581)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 265703 135570 923415 176880 244478 676109 685804 911559 022475 599505 903496 502766 839381 961447 574560 132289 > 9¹⁰⁰ [i]