MinT - Best Known (57, 57+95, s)-Nets in Base 8

Best Known (57, 57+95, s)-Nets in Base 8

(57, 57+95, 98)-Net over F₈ — Constructive and digital

Digital (57, 152, 98)-net over F₈, using

t-expansion [i] based on digital (37, 152, 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]

(57, 57+95, 144)-Net over F₈ — Digital

Digital (57, 152, 144)-net over F₈, using

t-expansion [i] based on digital (45, 152, 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]

(57, 57+95, 2061)-Net in Base 8 — Upper bound on s

There is no (57, 152, 2062)-net in base 8, because

1 times m-reduction [i] would yield (57, 151, 2062)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23404 866650 753204 787576 269256 112468 832445 835032 424122 407828 792710 248443 978731 204090 405885 240782 884825 464545 199999 927689 509966 346801 619968 > 8¹⁵¹ [i]