MinT - Best Known (42, 42+106, s)-Nets in Base 8

Best Known (42, 42+106, s)-Nets in Base 8

(42, 42+106, 98)-Net over F₈ — Constructive and digital

Digital (42, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(42, 42+106, 129)-Net over F₈ — Digital

Digital (42, 148, 129)-net over F₈, using

t-expansion [i] based on digital (38, 148, 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]

(42, 42+106, 945)-Net in Base 8 — Upper bound on s

There is no (42, 148, 946)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 47 434570 519590 817584 516741 735417 118736 587645 633853 807976 719513 272604 411767 589357 754558 004105 133045 389113 672975 122384 697529 801497 868384 > 8¹⁴⁸ [i]