MinT - Best Known (137−94, 137, s)-Nets in Base 8

Best Known (137−94, 137, s)-Nets in Base 8

(137−94, 137, 98)-Net over F₈ — Constructive and digital

Digital (43, 137, 98)-net over F₈, using

t-expansion [i] based on digital (37, 137, 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]

(137−94, 137, 129)-Net over F₈ — Digital

Digital (43, 137, 129)-net over F₈, using

t-expansion [i] based on digital (38, 137, 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]

(137−94, 137, 1096)-Net in Base 8 — Upper bound on s

There is no (43, 137, 1097)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5469 128017 334551 744093 655903 943730 269035 844241 699179 106993 678955 479781 827081 013012 974244 286404 432999 589365 354072 374481 108544 > 8¹³⁷ [i]