MinT - Best Known (152−107, 152, s)-Nets in Base 8

Best Known (152−107, 152, s)-Nets in Base 8

(152−107, 152, 98)-Net over F₈ — Constructive and digital

Digital (45, 152, 98)-net over F₈, using

t-expansion [i] based on digital (37, 152, 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]

(152−107, 152, 144)-Net over F₈ — Digital

Digital (45, 152, 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]

(152−107, 152, 1067)-Net in Base 8 — Upper bound on s

There is no (45, 152, 1068)-net in base 8, because

1 times m-reduction [i] would yield (45, 151, 1068)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23962 708673 877617 947412 468610 732609 862553 854930 600598 331657 614277 398554 126247 111307 093642 159661 616107 342295 162157 448766 266861 224385 411712 > 8¹⁵¹ [i]