MinT - Best Known (100−75, 100, s)-Nets in Base 16

Best Known (100−75, 100, s)-Nets in Base 16

(100−75, 100, 65)-Net over F₁₆ — Constructive and digital

Digital (25, 100, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 100, 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]

(100−75, 100, 76)-Net in Base 16 — Constructive

(25, 100, 76)-net in base 16, using

base change [i] based on digital (5, 80, 76)-net over F₃₂, using
- net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(100−75, 100, 144)-Net over F₁₆ — Digital

Digital (25, 100, 144)-net over F₁₆, using

net from sequence [i] based on digital (25, 143)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 25 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(100−75, 100, 1607)-Net in Base 16 — Upper bound on s

There is no (25, 100, 1608)-net in base 16, because

1 times m-reduction [i] would yield (25, 99, 1608)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 162865 064799 516370 003558 990033 320208 985666 603612 123816 655554 859315 908610 164526 306456 048158 553817 192578 622866 787860 337666 > 16⁹⁹ [i]