MinT - Best Known (154−105, 154, s)-Nets in Base 8

Best Known (154−105, 154, s)-Nets in Base 8

(154−105, 154, 98)-Net over F₈ — Constructive and digital

Digital (49, 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]

(154−105, 154, 144)-Net over F₈ — Digital

Digital (49, 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]

(154−105, 154, 1279)-Net in Base 8 — Upper bound on s

There is no (49, 154, 1280)-net in base 8, because

1 times m-reduction [i] would yield (49, 153, 1280)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 523067 618775 902554 550250 628683 775869 408318 246676 287631 483450 959797 218863 120550 918316 502139 128980 951711 841878 178521 558213 477708 354659 908281 > 8¹⁵³ [i]