MinT - Best Known (133−91, 133, s)-Nets in Base 8

Best Known (133−91, 133, s)-Nets in Base 8

(133−91, 133, 98)-Net over F₈ — Constructive and digital

Digital (42, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(133−91, 133, 129)-Net over F₈ — Digital

Digital (42, 133, 129)-net over F₈, using

t-expansion [i] based on digital (38, 133, 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]

(133−91, 133, 1094)-Net in Base 8 — Upper bound on s

There is no (42, 133, 1095)-net in base 8, because

1 times m-reduction [i] would yield (42, 132, 1095)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 166869 200733 007426 540634 341809 499435 825175 271462 112840 009977 622558 611753 440359 025739 939503 488090 488859 078611 734203 744752 > 8¹³² [i]