MinT - Best Known (54, 162, s)-Nets in Base 8

Best Known (54, 162, s)-Nets in Base 8

(54, 162, 98)-Net over F₈ — Constructive and digital

Digital (54, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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, 162, 144)-Net over F₈ — Digital

Digital (54, 162, 144)-net over F₈, using

t-expansion [i] based on digital (45, 162, 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, 162, 1499)-Net in Base 8 — Upper bound on s

There is no (54, 162, 1500)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 202 449082 125792 783883 252450 432134 177017 651525 421981 854578 545993 784194 890394 705859 928966 005119 192447 965804 591755 846970 594004 876434 014259 590773 686636 > 8¹⁶² [i]