MinT - Best Known (154−99, 154, s)-Nets in Base 8

Best Known (154−99, 154, s)-Nets in Base 8

(154−99, 154, 98)-Net over F₈ — Constructive and digital

Digital (55, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−99, 154, 144)-Net over F₈ — Digital

Digital (55, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(154−99, 154, 1772)-Net in Base 8 — Upper bound on s

There is no (55, 154, 1773)-net in base 8, because

1 times m-reduction [i] would yield (55, 153, 1773)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 511448 670619 218166 398574 845930 025711 029342 943019 612893 610176 001909 050257 792443 061237 377645 758412 773694 502462 310113 930284 804594 904383 955472 > 8¹⁵³ [i]