MinT - Best Known (54, 54+91, s)-Nets in Base 8

Best Known (54, 54+91, s)-Nets in Base 8

(54, 54+91, 98)-Net over F₈ — Constructive and digital

Digital (54, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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+91, 144)-Net over F₈ — Digital

Digital (54, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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+91, 1925)-Net in Base 8 — Upper bound on s

There is no (54, 145, 1926)-net in base 8, because

1 times m-reduction [i] would yield (54, 144, 1926)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11123 467950 352536 745149 575134 648202 734410 520472 504998 337430 315749 425038 050396 239369 014646 868480 159745 990672 747416 972574 722569 766032 > 8¹⁴⁴ [i]