MinT - Best Known (90−49, 90, s)-Nets in Base 8

Best Known (90−49, 90, s)-Nets in Base 8

(90−49, 90, 98)-Net over F₈ — Constructive and digital

Digital (41, 90, 98)-net over F₈, using

t-expansion [i] based on digital (37, 90, 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]

(90−49, 90, 129)-Net over F₈ — Digital

Digital (41, 90, 129)-net over F₈, using

t-expansion [i] based on digital (38, 90, 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]

(90−49, 90, 3112)-Net in Base 8 — Upper bound on s

There is no (41, 90, 3113)-net in base 8, because

1 times m-reduction [i] would yield (41, 89, 3113)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 237 540548 426855 036366 262155 328130 093643 957388 009921 099568 708714 287977 819211 535186 > 8⁸⁹ [i]