MinT - Best Known (103−82, 103, s)-Nets in Base 16

Best Known (103−82, 103, s)-Nets in Base 16

(103−82, 103, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 103, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 103, 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]

(103−82, 103, 129)-Net over F₁₆ — Digital

Digital (21, 103, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 103, 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]

(103−82, 103, 1117)-Net in Base 16 — Upper bound on s

There is no (21, 103, 1118)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10917 324859 645320 062829 751846 430562 984642 129366 315953 525626 224213 186000 775083 592285 178024 371654 741635 995924 298522 769134 446446 > 16¹⁰³ [i]