MinT - Best Known (81−64, 81, s)-Nets in Base 16

Best Known (81−64, 81, s)-Nets in Base 16

(81−64, 81, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 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]

(81−64, 81, 112)-Net over F₁₆ — Digital

Digital (17, 81, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(81−64, 81, 934)-Net in Base 16 — Upper bound on s

There is no (17, 81, 935)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 34 608803 784857 915619 843943 082863 147249 319505 810575 807020 035147 819527 719778 256790 078566 165409 914301 > 16⁸¹ [i]