MinT - Best Known (56, 169, s)-Nets in Base 8

Best Known (56, 169, s)-Nets in Base 8

(56, 169, 98)-Net over F₈ — Constructive and digital

Digital (56, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(56, 169, 144)-Net over F₈ — Digital

Digital (56, 169, 144)-net over F₈, using

t-expansion [i] based on digital (45, 169, 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]

(56, 169, 1552)-Net in Base 8 — Upper bound on s

There is no (56, 169, 1553)-net in base 8, because

1 times m-reduction [i] would yield (56, 168, 1553)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 119899 575770 257186 341952 072095 646282 682954 850254 747587 940817 278572 115088 571981 189835 594038 654301 972911 805334 271065 680512 437728 718004 164956 206379 522112 > 8¹⁶⁸ [i]