MinT - Best Known (113−65, 113, s)-Nets in Base 8

Best Known (113−65, 113, s)-Nets in Base 8

(113−65, 113, 98)-Net over F₈ — Constructive and digital

Digital (48, 113, 98)-net over F₈, using

t-expansion [i] based on digital (37, 113, 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]

(113−65, 113, 144)-Net over F₈ — Digital

Digital (48, 113, 144)-net over F₈, using

t-expansion [i] based on digital (45, 113, 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]

(113−65, 113, 2626)-Net in Base 8 — Upper bound on s

There is no (48, 113, 2627)-net in base 8, because

1 times m-reduction [i] would yield (48, 112, 2627)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 141651 860619 642321 875265 993172 275744 294706 413673 567936 027045 042032 831263 946438 860568 219674 533852 007574 > 8¹¹² [i]