MinT - Best Known (123−39, 123, s)-Nets in Base 16

Best Known (123−39, 123, s)-Nets in Base 16

(123−39, 123, 1034)-Net over F₁₆ — Constructive and digital

Digital (84, 123, 1034)-net over F₁₆, using

16¹ times duplication [i] based on digital (83, 122, 1034)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 40, 516)-net over F₁₆, using
    - trace code for nets [i] based on digital (1, 20, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-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, using
        Niederreiter sequence [i]

(123−39, 123, 7930)-Net over F₁₆ — Digital

Digital (84, 123, 7930)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−39, 123, large)-Net in Base 16 — Upper bound on s

There is no (84, 123, large)-net in base 16, because

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