MinT - Best Known (25, 81, s)-Nets in Base 16

Best Known (25, 81, s)-Nets in Base 16

(25, 81, 65)-Net over F₁₆ — Constructive and digital

Digital (25, 81, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 81, 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]

(25, 81, 98)-Net in Base 16 — Constructive

(25, 81, 98)-net in base 16, using

9 times m-reduction [i] based on (25, 90, 98)-net in base 16, using
- base change [i] based on digital (7, 72, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(25, 81, 144)-Net over F₁₆ — Digital

Digital (25, 81, 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]

(25, 81, 2276)-Net in Base 16 — Upper bound on s

There is no (25, 81, 2277)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 34 216167 942497 365721 237487 211663 091128 744095 008724 764743 536126 090806 532263 909407 087432 499913 353116 > 16⁸¹ [i]