MinT - Best Known (161−113, 161, s)-Nets in Base 8

Best Known (161−113, 161, s)-Nets in Base 8

(161−113, 161, 98)-Net over F₈ — Constructive and digital

Digital (48, 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]

(161−113, 161, 144)-Net over F₈ — Digital

Digital (48, 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]

(161−113, 161, 1144)-Net in Base 8 — Upper bound on s

There is no (48, 161, 1145)-net in base 8, because

1 times m-reduction [i] would yield (48, 160, 1145)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 182222 959913 124754 831025 256505 661355 831717 553261 523108 761061 857883 899660 416455 501612 717461 488093 539627 662163 942743 679993 847533 724447 675050 986931 > 8¹⁶⁰ [i]