MinT - Best Known (89, 89+40, s)-Nets in Base 16

Best Known (89, 89+40, s)-Nets in Base 16

(89, 89+40, 1036)-Net over F₁₆ — Constructive and digital

Digital (89, 129, 1036)-net over F₁₆, using

1 times m-reduction [i] based on digital (89, 130, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (24, 44, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 22, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (45, 86, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 43, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(89, 89+40, 9887)-Net over F₁₆ — Digital

Digital (89, 129, 9887)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+40, large)-Net in Base 16 — Upper bound on s

There is no (89, 129, large)-net in base 16, because

38 times m-reduction [i] would yield (89, 91, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]