MinT - Best Known (26, 26+75, s)-Nets in Base 16

Best Known (26, 26+75, s)-Nets in Base 16

(26, 26+75, 65)-Net over F₁₆ — Constructive and digital

Digital (26, 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]

(26, 26+75, 76)-Net in Base 16 — Constructive

(26, 101, 76)-net in base 16, using

4 times m-reduction [i] based on (26, 105, 76)-net in base 16, using
- base change [i] based on digital (5, 84, 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]

(26, 26+75, 150)-Net over F₁₆ — Digital

Digital (26, 101, 150)-net over F₁₆, using

net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
  - a curve from the manYPoints database [i]

(26, 26+75, 1734)-Net in Base 16 — Upper bound on s

There is no (26, 101, 1735)-net in base 16, because

1 times m-reduction [i] would yield (26, 100, 1735)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 621942 043792 808145 362025 915700 384347 022009 904752 468693 966065 273073 860731 720206 334878 605191 512864 118531 868280 264781 734676 > 16¹⁰⁰ [i]