MinT - Best Known (54, 54+99, s)-Nets in Base 8

Best Known (54, 54+99, s)-Nets in Base 8

(54, 54+99, 98)-Net over F₈ — Constructive and digital

Digital (54, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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]

(54, 54+99, 144)-Net over F₈ — Digital

Digital (54, 153, 144)-net over F₈, using

t-expansion [i] based on digital (45, 153, 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]

(54, 54+99, 1697)-Net in Base 8 — Upper bound on s

There is no (54, 153, 1698)-net in base 8, because

1 times m-reduction [i] would yield (54, 152, 1698)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 188621 209084 895444 433535 568520 608663 703552 767662 572897 158033 765228 084050 662525 407351 380702 356143 084425 177359 389485 895120 515179 292740 289848 > 8¹⁵² [i]