MinT - Best Known (48, 48+92, s)-Nets in Base 8

Best Known (48, 48+92, s)-Nets in Base 8

(48, 48+92, 98)-Net over F₈ — Constructive and digital

Digital (48, 140, 98)-net over F₈, using

t-expansion [i] based on digital (37, 140, 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+92, 144)-Net over F₈ — Digital

Digital (48, 140, 144)-net over F₈, using

t-expansion [i] based on digital (45, 140, 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+92, 1412)-Net in Base 8 — Upper bound on s

There is no (48, 140, 1413)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 785365 455931 878216 526925 003372 641626 407153 457662 358866 296633 834381 517977 046243 909663 452916 170784 893708 413853 844248 774747 912000 > 8¹⁴⁰ [i]