MinT - Best Known (84, 84+37, s)-Nets in Base 16

Best Known (84, 84+37, s)-Nets in Base 16

(84, 84+37, 1038)-Net over F₁₆ — Constructive and digital

Digital (84, 121, 1038)-net over F₁₆, using

16¹ times duplication [i] based on digital (83, 120, 1038)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (22, 40, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 20, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (43, 80, 520)-net over F₁₆, using
    - trace code for nets [i] based on digital (3, 40, 260)-net over F₂₅₆, using
      - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(84, 84+37, 10631)-Net over F₁₆ — Digital

Digital (84, 121, 10631)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+37, large)-Net in Base 16 — Upper bound on s

There is no (84, 121, large)-net in base 16, because

35 times m-reduction [i] would yield (84, 86, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]