MinT - Best Known (46−41, 46, s)-Nets in Base 49

Best Known (46−41, 46, s)-Nets in Base 49

(46−41, 46, 55)-Net over F₄₉ — Constructive and digital

Digital (5, 46, 55)-net over F₄₉, using

net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
- Niederreiter sequence [i]

(46−41, 46, 92)-Net over F₄₉ — Digital

Digital (5, 46, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 46, 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]

(46−41, 46, 1089)-Net in Base 49 — Upper bound on s

There is no (5, 46, 1090)-net in base 49, because

1 times m-reduction [i] would yield (5, 45, 1090)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 11634 496040 315395 802362 481286 498161 491368 662107 850787 882266 957117 069074 416001 > 49⁴⁵ [i]