MinT - Best Known (47, 47+57, s)-Nets in Base 8

Best Known (47, 47+57, s)-Nets in Base 8

(47, 47+57, 98)-Net over F₈ — Constructive and digital

Digital (47, 104, 98)-net over F₈, using

t-expansion [i] based on digital (37, 104, 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]

(47, 47+57, 144)-Net over F₈ — Digital

Digital (47, 104, 144)-net over F₈, using

t-expansion [i] based on digital (45, 104, 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]

(47, 47+57, 3370)-Net in Base 8 — Upper bound on s

There is no (47, 104, 3371)-net in base 8, because

1 times m-reduction [i] would yield (47, 103, 3371)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1044 033219 925219 536163 085165 540919 602319 285647 652935 211567 750093 936547 331867 261385 885683 712792 > 8¹⁰³ [i]