MinT - Best Known (86, 86+39, s)-Nets in Base 16

Best Known (86, 86+39, s)-Nets in Base 16

(86, 86+39, 1036)-Net over F₁₆ — Constructive and digital

Digital (86, 125, 1036)-net over F₁₆, using

16¹ times duplication [i] based on digital (85, 124, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (23, 42, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 21, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (43, 82, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 41, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(86, 86+39, 9173)-Net over F₁₆ — Digital

Digital (86, 125, 9173)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+39, large)-Net in Base 16 — Upper bound on s

There is no (86, 125, large)-net in base 16, because

37 times m-reduction [i] would yield (86, 88, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]