MinT - Best Known (54−21, 54, s)-Nets in Base 49

Best Known (54−21, 54, s)-Nets in Base 49

(54−21, 54, 396)-Net over F₄₉ — Constructive and digital

Digital (33, 54, 396)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 12, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (21, 42, 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]

(54−21, 54, 6343)-Net over F₄₉ — Digital

Digital (33, 54, 6343)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−21, 54, large)-Net in Base 49 — Upper bound on s

There is no (33, 54, large)-net in base 49, because

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