MinT - Best Known (56, 167, s)-Nets in Base 8

Best Known (56, 167, s)-Nets in Base 8

(56, 167, 98)-Net over F₈ — Constructive and digital

Digital (56, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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, 167, 144)-Net over F₈ — Digital

Digital (56, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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, 167, 1586)-Net in Base 8 — Upper bound on s

There is no (56, 167, 1587)-net in base 8, because

1 times m-reduction [i] would yield (56, 166, 1587)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 839630 373778 420884 717663 009624 812157 796516 652403 360735 691373 084458 435792 700900 081472 149413 625824 683014 908989 346876 507087 531058 666037 722236 328989 136384 > 8¹⁶⁶ [i]