MinT - Best Known (161−111, 161, s)-Nets in Base 8

Best Known (161−111, 161, s)-Nets in Base 8

(161−111, 161, 98)-Net over F₈ — Constructive and digital

Digital (50, 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]

(161−111, 161, 144)-Net over F₈ — Digital

Digital (50, 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]

(161−111, 161, 1257)-Net in Base 8 — Upper bound on s

There is no (50, 161, 1258)-net in base 8, because

1 times m-reduction [i] would yield (50, 160, 1258)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 212059 538372 799711 349885 335839 099582 872176 627609 299661 674970 531388 560291 834575 308338 713363 831570 867903 973342 407420 512467 025780 202267 418077 593840 > 8¹⁶⁰ [i]