MinT - Best Known (70, 70+33, s)-Nets in Base 16

Best Known (70, 70+33, s)-Nets in Base 16

(70, 70+33, 1032)-Net over F₁₆ — Constructive and digital

Digital (70, 103, 1032)-net over F₁₆, using

16¹ times duplication [i] based on digital (69, 102, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 34, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 17, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (35, 68, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 34, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(70, 70+33, 6421)-Net over F₁₆ — Digital

Digital (70, 103, 6421)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+33, large)-Net in Base 16 — Upper bound on s

There is no (70, 103, large)-net in base 16, because

31 times m-reduction [i] would yield (70, 72, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]