MinT - Best Known (88−27, 88, s)-Nets in Base 16

Best Known (88−27, 88, s)-Nets in Base 16

(88−27, 88, 1036)-Net over F₁₆ — Constructive and digital

Digital (61, 88, 1036)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (17, 30, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 15, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]
2. digital (31, 58, 518)-net over F₁₆, using
  - trace code for nets [i] based on digital (2, 29, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(88−27, 88, 8382)-Net over F₁₆ — Digital

Digital (61, 88, 8382)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−27, 88, large)-Net in Base 16 — Upper bound on s

There is no (61, 88, large)-net in base 16, because

25 times m-reduction [i] would yield (61, 63, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]