MinT - Best Known (152−112, 152, s)-Nets in Base 8

Best Known (152−112, 152, s)-Nets in Base 8

(152−112, 152, 98)-Net over F₈ — Constructive and digital

Digital (40, 152, 98)-net over F₈, using

t-expansion [i] based on digital (37, 152, 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]

(152−112, 152, 129)-Net over F₈ — Digital

Digital (40, 152, 129)-net over F₈, using

t-expansion [i] based on digital (38, 152, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(152−112, 152, 841)-Net in Base 8 — Upper bound on s

There is no (40, 152, 842)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 192126 352526 430547 143268 059696 990564 195417 016200 645517 518929 505563 041759 585846 636334 258090 079306 994132 389062 409170 502007 269443 865295 157860 > 8¹⁵² [i]