MinT - Best Known (154−113, 154, s)-Nets in Base 8

Best Known (154−113, 154, s)-Nets in Base 8

(154−113, 154, 98)-Net over F₈ — Constructive and digital

Digital (41, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−113, 154, 129)-Net over F₈ — Digital

Digital (41, 154, 129)-net over F₈, using

t-expansion [i] based on digital (38, 154, 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]

(154−113, 154, 874)-Net in Base 8 — Upper bound on s

There is no (41, 154, 875)-net in base 8, because

1 times m-reduction [i] would yield (41, 153, 875)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 521472 860483 530927 921921 101740 042629 203449 475205 609315 391953 450264 241106 011764 897254 847205 991735 015880 436661 284804 857240 256759 418543 820036 > 8¹⁵³ [i]