MinT - Best Known (111−34, 111, s)-Nets in Base 16

Best Known (111−34, 111, s)-Nets in Base 16

(111−34, 111, 1036)-Net over F₁₆ — Constructive and digital

Digital (77, 111, 1036)-net over F₁₆, using

1 times m-reduction [i] based on digital (77, 112, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 38, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 19, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (39, 74, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 37, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(111−34, 111, 9868)-Net over F₁₆ — Digital

Digital (77, 111, 9868)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−34, 111, large)-Net in Base 16 — Upper bound on s

There is no (77, 111, large)-net in base 16, because

32 times m-reduction [i] would yield (77, 79, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]