MinT - Best Known (20, 101, s)-Nets in Base 16

Best Known (20, 101, s)-Nets in Base 16

(20, 101, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 101, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 101, 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]

(20, 101, 129)-Net over F₁₆ — Digital

Digital (20, 101, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 101, 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]

(20, 101, 1054)-Net in Base 16 — Upper bound on s

There is no (20, 101, 1055)-net in base 16, because

1 times m-reduction [i] would yield (20, 100, 1055)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 639393 547464 724760 992451 526549 621820 972240 081075 666668 948267 597874 714091 726931 069011 420417 834302 581167 515665 844186 537376 > 16¹⁰⁰ [i]