MinT - Best Known (173−118, 173, s)-Nets in Base 8

Best Known (173−118, 173, s)-Nets in Base 8

(173−118, 173, 98)-Net over F₈ — Constructive and digital

Digital (55, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(173−118, 173, 144)-Net over F₈ — Digital

Digital (55, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(173−118, 173, 1412)-Net in Base 8 — Upper bound on s

There is no (55, 173, 1413)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 745545 481301 446324 506435 342853 885752 672739 098219 943776 968696 977107 255733 610119 239446 225801 654620 461632 196256 902230 760760 393887 899712 869490 207597 644350 193728 > 8¹⁷³ [i]