MinT - Best Known (15, 15+39, s)-Nets in Base 49

Best Known (15, 15+39, s)-Nets in Base 49

(15, 15+39, 65)-Net over F₄₉ — Constructive and digital

Digital (15, 54, 65)-net over F₄₉, using

net from sequence [i] based on digital (15, 64)-sequence over F₄₉, using
- Niederreiter sequence [i]

(15, 15+39, 92)-Net over F₄₉ — Digital

Digital (15, 54, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 54, 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]

(15, 15+39, 8555)-Net in Base 49 — Upper bound on s

There is no (15, 54, 8556)-net in base 49, because

1 times m-reduction [i] would yield (15, 53, 8556)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 380792 259969 208582 242139 999787 654989 684747 945835 669826 688239 323687 306083 895839 681375 357633 > 49⁵³ [i]