MinT - Best Known (146−86, 146, s)-Nets in Base 8

Best Known (146−86, 146, s)-Nets in Base 8

(146−86, 146, 98)-Net over F₈ — Constructive and digital

Digital (60, 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]

(146−86, 146, 144)-Net over F₈ — Digital

Digital (60, 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]

(146−86, 146, 2782)-Net in Base 8 — Upper bound on s

There is no (60, 146, 2783)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 712625 876457 935597 524768 394568 941802 899778 856036 191046 923872 360148 999054 885354 152996 979919 898275 358672 827716 469765 226818 815100 019640 > 8¹⁴⁶ [i]