MinT - Best Known (113−91, 113, s)-Nets in Base 16

Best Known (113−91, 113, s)-Nets in Base 16

(113−91, 113, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 113, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 113, 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]

(113−91, 113, 129)-Net over F₁₆ — Digital

Digital (22, 113, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 113, 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]

(113−91, 113, 1141)-Net in Base 16 — Upper bound on s

There is no (22, 113, 1142)-net in base 16, because

1 times m-reduction [i] would yield (22, 112, 1142)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 728 242980 339366 970446 258091 765447 915054 210050 307109 788924 578739 079642 422287 610822 721536 766761 336580 312331 378479 454482 755334 066193 169726 > 16¹¹² [i]