MinT - Best Known (48, 48+85, s)-Nets in Base 8

Best Known (48, 48+85, s)-Nets in Base 8

(48, 48+85, 98)-Net over F₈ — Constructive and digital

Digital (48, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(48, 48+85, 144)-Net over F₈ — Digital

Digital (48, 133, 144)-net over F₈, using

t-expansion [i] based on digital (45, 133, 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]

(48, 48+85, 1599)-Net in Base 8 — Upper bound on s

There is no (48, 133, 1600)-net in base 8, because

1 times m-reduction [i] would yield (48, 132, 1600)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 165061 008085 984017 887773 163966 552894 977405 893769 332356 804683 939733 752575 104969 552385 324959 855183 735052 441524 943087 828299 > 8¹³² [i]