MinT - Best Known (75, 124, s)-Nets in Base 9

Best Known (75, 124, s)-Nets in Base 9

(75, 124, 448)-Net over F₉ — Constructive and digital

Digital (75, 124, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 62, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(75, 124, 697)-Net over F₉ — Digital

Digital (75, 124, 697)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 124, 95213)-Net in Base 9 — Upper bound on s

There is no (75, 124, 95214)-net in base 9, because

1 times m-reduction [i] would yield (75, 123, 95214)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 293431 089802 389329 459531 613575 910371 488568 453055 123113 939539 685798 729809 107784 404103 852023 830875 270627 190981 635969 > 9¹²³ [i]