MinT - Best Known (11, 11+39, s)-Nets in Base 49

Best Known (11, 11+39, s)-Nets in Base 49

(11, 11+39, 61)-Net over F₄₉ — Constructive and digital

Digital (11, 50, 61)-net over F₄₉, using

net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
- Niederreiter sequence [i]

(11, 11+39, 92)-Net over F₄₉ — Digital

Digital (11, 50, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 50, 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]

(11, 11+39, 3765)-Net in Base 49 — Upper bound on s

There is no (11, 50, 3766)-net in base 49, because

1 times m-reduction [i] would yield (11, 49, 3766)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 66185 896315 455957 443244 689329 110091 381570 387904 575697 704005 531240 575644 359520 423777 > 49⁴⁹ [i]