MinT - Best Known (143−104, 143, s)-Nets in Base 8

Best Known (143−104, 143, s)-Nets in Base 8

(143−104, 143, 98)-Net over F₈ — Constructive and digital

Digital (39, 143, 98)-net over F₈, using

t-expansion [i] based on digital (37, 143, 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]

(143−104, 143, 129)-Net over F₈ — Digital

Digital (39, 143, 129)-net over F₈, using

t-expansion [i] based on digital (38, 143, 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]

(143−104, 143, 847)-Net in Base 8 — Upper bound on s

There is no (39, 143, 848)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1465 314247 614755 159135 582820 049779 629785 155018 922156 877948 609946 415590 637716 644792 242388 283406 122795 471918 731424 868883 903882 913204 > 8¹⁴³ [i]