MinT - Best Known (41, 168, s)-Nets in Base 8

Best Known (41, 168, s)-Nets in Base 8

(41, 168, 98)-Net over F₈ — Constructive and digital

Digital (41, 168, 98)-net over F₈, using

t-expansion [i] based on digital (37, 168, 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]

(41, 168, 129)-Net over F₈ — Digital

Digital (41, 168, 129)-net over F₈, using

t-expansion [i] based on digital (38, 168, 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]

(41, 168, 820)-Net in Base 8 — Upper bound on s

There is no (41, 168, 821)-net in base 8, because

1 times m-reduction [i] would yield (41, 167, 821)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 785690 817388 061123 859480 487567 256696 220145 819242 130824 975871 722514 483481 122210 487026 172533 620686 469563 511653 970255 596390 501368 861398 631166 210236 863744 > 8¹⁶⁷ [i]