MinT - Best Known (153, 153+31, s)-Nets in Base 4

Best Known (153, 153+31, s)-Nets in Base 4

(153, 153+31, 2056)-Net over F₄ — Constructive and digital

Digital (153, 184, 2056)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (45, 60, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 15, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
2. digital (93, 124, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 31, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(153, 153+31, 19798)-Net over F₄ — Digital

Digital (153, 184, 19798)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+31, large)-Net in Base 4 — Upper bound on s

There is no (153, 184, large)-net in base 4, because

29 times m-reduction [i] would yield (153, 155, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]