MinT - Best Known (74, 74+33, s)-Nets in Base 16

Best Known (74, 74+33, s)-Nets in Base 16

(74, 74+33, 1036)-Net over F₁₆ — Constructive and digital

Digital (74, 107, 1036)-net over F₁₆, using

16¹ times duplication [i] based on digital (73, 106, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (20, 36, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 18, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (37, 70, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 35, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(74, 74+33, 9075)-Net over F₁₆ — Digital

Digital (74, 107, 9075)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+33, large)-Net in Base 16 — Upper bound on s

There is no (74, 107, large)-net in base 16, because

31 times m-reduction [i] would yield (74, 76, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]