MinT - Best Known (47, 47+90, s)-Nets in Base 8

Best Known (47, 47+90, s)-Nets in Base 8

(47, 47+90, 98)-Net over F₈ — Constructive and digital

Digital (47, 137, 98)-net over F₈, using

t-expansion [i] based on digital (37, 137, 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+90, 144)-Net over F₈ — Digital

Digital (47, 137, 144)-net over F₈, using

t-expansion [i] based on digital (45, 137, 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+90, 1385)-Net in Base 8 — Upper bound on s

There is no (47, 137, 1386)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5313 282174 165536 373767 433340 213870 886787 373413 215615 009326 499340 855103 248584 472382 007067 232489 063461 803017 396914 871752 121232 > 8¹³⁷ [i]