MinT - Best Known (93−26, 93, s)-Nets in Base 16

Best Known (93−26, 93, s)-Nets in Base 16

(93−26, 93, 1285)-Net over F₁₆ — Constructive and digital

Digital (67, 93, 1285)-net over F₁₆, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 15, 257)-net over F₁₆, using
  - base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
2. digital (13, 26, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 13, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
3. digital (26, 52, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 26, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(93−26, 93, 20470)-Net over F₁₆ — Digital

Digital (67, 93, 20470)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−26, 93, large)-Net in Base 16 — Upper bound on s

There is no (67, 93, large)-net in base 16, because

24 times m-reduction [i] would yield (67, 69, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]