MinT - Best Known (97−31, 97, s)-Nets in Base 16

Best Known (97−31, 97, s)-Nets in Base 16

(97−31, 97, 1032)-Net over F₁₆ — Constructive and digital

Digital (66, 97, 1032)-net over F₁₆, using

16¹ times duplication [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)

(97−31, 97, 6296)-Net over F₁₆ — Digital

Digital (66, 97, 6296)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−31, 97, large)-Net in Base 16 — Upper bound on s

There is no (66, 97, large)-net in base 16, because

29 times m-reduction [i] would yield (66, 68, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]