MinT - Best Known (50, 50+60, s)-Nets in Base 8

Best Known (50, 50+60, s)-Nets in Base 8

(50, 50+60, 98)-Net over F₈ — Constructive and digital

Digital (50, 110, 98)-net over F₈, using

t-expansion [i] based on digital (37, 110, 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]

(50, 50+60, 144)-Net over F₈ — Digital

Digital (50, 110, 144)-net over F₈, using

t-expansion [i] based on digital (45, 110, 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]

(50, 50+60, 3505)-Net in Base 8 — Upper bound on s

There is no (50, 110, 3506)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2203 683434 444384 327485 656826 988030 166157 916000 810648 915626 988745 327831 768417 189785 089237 397977 799280 > 8¹¹⁰ [i]