MinT - Best Known (42, 42+19, s)-Nets in Base 16

Best Known (42, 42+19, s)-Nets in Base 16

(42, 42+19, 1032)-Net over F₁₆ — Constructive and digital

Digital (42, 61, 1032)-net over F₁₆, using

16¹ times duplication [i] based on digital (41, 60, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 20, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 10, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (21, 40, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 20, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(42, 42+19, 6072)-Net over F₁₆ — Digital

Digital (42, 61, 6072)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+19, large)-Net in Base 16 — Upper bound on s

There is no (42, 61, large)-net in base 16, because

17 times m-reduction [i] would yield (42, 44, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]