MinT - Best Known (93−73, 93, s)-Nets in Base 16

Best Known (93−73, 93, s)-Nets in Base 16

(93−73, 93, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 93, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 93, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(93−73, 93, 129)-Net over F₁₆ — Digital

Digital (20, 93, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 93, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(93−73, 93, 1117)-Net in Base 16 — Upper bound on s

There is no (20, 93, 1118)-net in base 16, because

1 times m-reduction [i] would yield (20, 92, 1118)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 612 789167 535152 325215 895120 978781 109012 314861 926403 618400 839709 005808 228145 998323 304589 901224 309724 483108 039846 > 16⁹² [i]