MinT - Best Known (160−107, 160, s)-Nets in Base 8

Best Known (160−107, 160, s)-Nets in Base 8

(160−107, 160, 98)-Net over F₈ — Constructive and digital

Digital (53, 160, 98)-net over F₈, using

t-expansion [i] based on digital (37, 160, 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]

(160−107, 160, 144)-Net over F₈ — Digital

Digital (53, 160, 144)-net over F₈, using

t-expansion [i] based on digital (45, 160, 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]

(160−107, 160, 1473)-Net in Base 8 — Upper bound on s

There is no (53, 160, 1474)-net in base 8, because

1 times m-reduction [i] would yield (53, 159, 1474)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 402317 263681 651269 339041 305369 725359 761458 441987 388097 350094 597505 958080 662326 218273 034188 576016 313249 695851 282087 951647 827173 154796 096922 730960 > 8¹⁵⁹ [i]