MinT - Best Known (54, 54+78, s)-Nets in Base 8

Best Known (54, 54+78, s)-Nets in Base 8

(54, 54+78, 98)-Net over F₈ — Constructive and digital

Digital (54, 132, 98)-net over F₈, using

t-expansion [i] based on digital (37, 132, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(54, 54+78, 144)-Net over F₈ — Digital

Digital (54, 132, 144)-net over F₈, using

t-expansion [i] based on digital (45, 132, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(54, 54+78, 2481)-Net in Base 8 — Upper bound on s

There is no (54, 132, 2482)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 163255 172741 294939 113972 825249 468533 833793 425073 213594 257992 859858 691658 401280 055175 770957 741288 545653 060626 136527 456472 > 8¹³² [i]