MinT - Best Known (161−97, 161, s)-Nets in Base 8

Best Known (161−97, 161, s)-Nets in Base 8

(161−97, 161, 98)-Net over F₈ — Constructive and digital

Digital (64, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(161−97, 161, 144)-Net over F₈ — Digital

Digital (64, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(161−97, 161, 2711)-Net in Base 8 — Upper bound on s

There is no (64, 161, 2712)-net in base 8, because

1 times m-reduction [i] would yield (64, 160, 2712)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 162109 379819 034427 392605 788872 163947 531036 993819 547624 722587 144830 290244 037492 935071 485415 368842 502197 972805 773483 459326 043631 741250 442868 827716 > 8¹⁶⁰ [i]