MinT - Best Known (45, 45+112, s)-Nets in Base 8

Best Known (45, 45+112, s)-Nets in Base 8

(45, 45+112, 98)-Net over F₈ — Constructive and digital

Digital (45, 157, 98)-net over F₈, using

t-expansion [i] based on digital (37, 157, 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]

(45, 45+112, 144)-Net over F₈ — Digital

Digital (45, 157, 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]

(45, 45+112, 1020)-Net in Base 8 — Upper bound on s

There is no (45, 157, 1021)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6340 178170 692644 703035 085739 212318 001508 908820 901604 456158 506998 238116 783684 112440 442122 939142 929625 889416 834109 306554 374962 664925 195796 340637 > 8¹⁵⁷ [i]