MinT - Best Known (43, 43+107, s)-Nets in Base 8

Best Known (43, 43+107, s)-Nets in Base 8

(43, 43+107, 98)-Net over F₈ — Constructive and digital

Digital (43, 150, 98)-net over F₈, using

t-expansion [i] based on digital (37, 150, 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]

(43, 43+107, 129)-Net over F₈ — Digital

Digital (43, 150, 129)-net over F₈, using

t-expansion [i] based on digital (38, 150, 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]

(43, 43+107, 984)-Net in Base 8 — Upper bound on s

There is no (43, 150, 985)-net in base 8, because

1 times m-reduction [i] would yield (43, 149, 985)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 376 126652 629720 271084 726040 442659 156077 493529 602668 985644 558767 900168 445295 720861 788984 282966 699413 527969 109423 125306 362403 918715 847216 > 8¹⁴⁹ [i]