MinT - Best Known (140−82, 140, s)-Nets in Base 8

Best Known (140−82, 140, s)-Nets in Base 8

(140−82, 140, 98)-Net over F₈ — Constructive and digital

Digital (58, 140, 98)-net over F₈, using

t-expansion [i] based on digital (37, 140, 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]

(140−82, 140, 144)-Net over F₈ — Digital

Digital (58, 140, 144)-net over F₈, using

t-expansion [i] based on digital (45, 140, 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]

(140−82, 140, 2770)-Net in Base 8 — Upper bound on s

There is no (58, 140, 2771)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 739113 762821 765941 313161 596245 839496 554040 839136 867978 290087 475224 403385 976695 391778 639585 397655 680357 117132 962965 246022 345704 > 8¹⁴⁰ [i]