MinT - Best Known (56, 56+90, s)-Nets in Base 8

Best Known (56, 56+90, s)-Nets in Base 8

(56, 56+90, 98)-Net over F₈ — Constructive and digital

Digital (56, 146, 98)-net over F₈, using

t-expansion [i] based on digital (37, 146, 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, 56+90, 144)-Net over F₈ — Digital

Digital (56, 146, 144)-net over F₈, using

t-expansion [i] based on digital (45, 146, 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, 56+90, 2115)-Net in Base 8 — Upper bound on s

There is no (56, 146, 2116)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 723738 531054 353001 765909 463818 572732 061974 300382 808502 924296 757215 017463 475662 410980 690774 156704 311400 558001 758397 202809 075050 952848 > 8¹⁴⁶ [i]