MinT - Best Known (101−77, 101, s)-Nets in Base 16

Best Known (101−77, 101, s)-Nets in Base 16

(101−77, 101, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 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]

(101−77, 101, 129)-Net over F₁₆ — Digital

Digital (24, 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]

(101−77, 101, 1456)-Net in Base 16 — Upper bound on s

There is no (24, 101, 1457)-net in base 16, because

1 times m-reduction [i] would yield (24, 100, 1457)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 630992 259179 297736 099285 811107 365514 903591 042851 724423 618674 930056 175208 902100 147524 191278 289276 272534 483433 138108 981016 > 16¹⁰⁰ [i]