MinT - Best Known (108−65, 108, s)-Nets in Base 8

Best Known (108−65, 108, s)-Nets in Base 8

(108−65, 108, 98)-Net over F₈ — Constructive and digital

Digital (43, 108, 98)-net over F₈, using

t-expansion [i] based on digital (37, 108, 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]

(108−65, 108, 129)-Net over F₈ — Digital

Digital (43, 108, 129)-net over F₈, using

t-expansion [i] based on digital (38, 108, 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]

(108−65, 108, 1891)-Net in Base 8 — Upper bound on s

There is no (43, 108, 1892)-net in base 8, because

1 times m-reduction [i] would yield (43, 107, 1892)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 271980 818463 905658 683003 362050 578174 116493 304982 963404 346751 586703 920401 281957 640923 345909 046087 > 8¹⁰⁷ [i]