MinT - Best Known (67−21, 67, s)-Nets in Base 16

Best Known (67−21, 67, s)-Nets in Base 16

(67−21, 67, 1032)-Net over F₁₆ — Constructive and digital

Digital (46, 67, 1032)-net over F₁₆, using

16¹ times duplication [i] based on digital (45, 66, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 22, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 11, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (23, 44, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 22, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(67−21, 67, 5994)-Net over F₁₆ — Digital

Digital (46, 67, 5994)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−21, 67, large)-Net in Base 16 — Upper bound on s

There is no (46, 67, large)-net in base 16, because

19 times m-reduction [i] would yield (46, 48, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]