MinT - Best Known (8, 8+24, s)-Nets in Base 49

Best Known (8, 8+24, s)-Nets in Base 49

(8, 8+24, 58)-Net over F₄₉ — Constructive and digital

Digital (8, 32, 58)-net over F₄₉, using

net from sequence [i] based on digital (8, 57)-sequence over F₄₉, using
- Niederreiter sequence [i]

(8, 8+24, 92)-Net over F₄₉ — Digital

Digital (8, 32, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 32, 92)-net over F₄₉, using
- net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(8, 8+24, 3536)-Net in Base 49 — Upper bound on s

There is no (8, 32, 3537)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 1 220789 846690 894547 122027 261437 236693 812909 276298 844225 > 49³² [i]