MinT - Best Known (171−125, 171, s)-Nets in Base 8

Best Known (171−125, 171, s)-Nets in Base 8

(171−125, 171, 98)-Net over F₈ — Constructive and digital

Digital (46, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−125, 171, 144)-Net over F₈ — Digital

Digital (46, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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]

(171−125, 171, 984)-Net in Base 8 — Upper bound on s

There is no (46, 171, 985)-net in base 8, because

1 times m-reduction [i] would yield (46, 170, 985)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3422 331055 407533 673271 314882 750791 418286 220090 506035 217900 627490 650901 716097 183053 246782 281030 224082 237290 963960 042777 100842 746104 103401 369426 445857 126816 > 8¹⁷⁰ [i]