MinT - Best Known (171−98, 171, s)-Nets in Base 8

Best Known (171−98, 171, s)-Nets in Base 8

(171−98, 171, 111)-Net over F₈ — Constructive and digital

Digital (73, 171, 111)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (10, 59, 46)-net over F₈, using
  - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
2. digital (14, 112, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(171−98, 171, 159)-Net over F₈ — Digital

Digital (73, 171, 159)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−98, 171, 162)-Net in Base 8

(73, 171, 162)-net in base 8, using

1 times m-reduction [i] based on (73, 172, 162)-net in base 8, using
- base change [i] based on digital (30, 129, 162)-net over F₁₆, using
  - net from sequence [i] based on digital (30, 161)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 30 and N(F) ≥ 162, using
      - a curve from the manYPoints database [i]

(171−98, 171, 3839)-Net in Base 8 — Upper bound on s

There is no (73, 171, 3840)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26830 032594 095763 429278 635329 920873 885675 254375 240062 954320 790990 133187 401728 143009 963754 093843 670923 362009 657626 306003 776849 739233 647974 180427 334530 708841 > 8¹⁷¹ [i]