MinT - Best Known (69, 69+31, s)-Nets in Base 16

Best Known (69, 69+31, s)-Nets in Base 16

(69, 69+31, 1036)-Net over F₁₆ — Constructive and digital

Digital (69, 100, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (19, 34, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 17, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (35, 66, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 33, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(69, 69+31, 8303)-Net over F₁₆ — Digital

Digital (69, 100, 8303)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+31, large)-Net in Base 16 — Upper bound on s

There is no (69, 100, large)-net in base 16, because

29 times m-reduction [i] would yield (69, 71, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]