MinT - Best Known (55−22, 55, s)-Nets in Base 49

Best Known (55−22, 55, s)-Nets in Base 49

(55−22, 55, 395)-Net over F₄₉ — Constructive and digital

Digital (33, 55, 395)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 12, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (21, 43, 344)-net over F₄₉, using
  - net from sequence [i] based on digital (21, 343)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 21 and N(F) ≥ 344, using
      - the Hermitian function field over F₄₉ [i]

(55−22, 55, 4841)-Net over F₄₉ — Digital

Digital (33, 55, 4841)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−22, 55, large)-Net in Base 49 — Upper bound on s

There is no (33, 55, large)-net in base 49, because

20 times m-reduction [i] would yield (33, 35, large)-net in base 49, but
- mutually orthogonal hypercube bound [i]