MinT - Best Known (107−63, 107, s)-Nets in Base 8

Best Known (107−63, 107, s)-Nets in Base 8

(107−63, 107, 98)-Net over F₈ — Constructive and digital

Digital (44, 107, 98)-net over F₈, using

t-expansion [i] based on digital (37, 107, 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]

(107−63, 107, 130)-Net over F₈ — Digital

Digital (44, 107, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(107−63, 107, 2152)-Net in Base 8 — Upper bound on s

There is no (44, 107, 2153)-net in base 8, because

1 times m-reduction [i] would yield (44, 106, 2153)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534562 750955 260991 165542 310753 424733 347764 260113 350924 856013 764431 461838 628775 009181 643545 559840 > 8¹⁰⁶ [i]