MinT - Best Known (42, 42+117, s)-Nets in Base 8

Best Known (42, 42+117, s)-Nets in Base 8

(42, 42+117, 98)-Net over F₈ — Constructive and digital

Digital (42, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(42, 42+117, 129)-Net over F₈ — Digital

Digital (42, 159, 129)-net over F₈, using

t-expansion [i] based on digital (38, 159, 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]

(42, 42+117, 888)-Net in Base 8 — Upper bound on s

There is no (42, 159, 889)-net in base 8, because

1 times m-reduction [i] would yield (42, 158, 889)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 49007 526931 434589 085023 879576 116285 924184 162317 349007 739468 001712 189885 635653 200811 989631 624105 428030 845757 484718 991606 216736 400455 693979 476320 > 8¹⁵⁸ [i]