MinT - Best Known (65, 65+30, s)-Nets in Base 16

Best Known (65, 65+30, s)-Nets in Base 16

(65, 65+30, 1032)-Net over F₁₆ — Constructive and digital

Digital (65, 95, 1032)-net over F₁₆, using

1 times m-reduction [i] based on digital (65, 96, 1032)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 32, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 16, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (33, 64, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 32, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(65, 65+30, 6862)-Net over F₁₆ — Digital

Digital (65, 95, 6862)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+30, large)-Net in Base 16 — Upper bound on s

There is no (65, 95, large)-net in base 16, because

28 times m-reduction [i] would yield (65, 67, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]