MinT - Best Known (110−89, 110, s)-Nets in Base 16

Best Known (110−89, 110, s)-Nets in Base 16

(110−89, 110, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 110, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 110, 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]

(110−89, 110, 129)-Net over F₁₆ — Digital

Digital (21, 110, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 110, 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]

(110−89, 110, 1081)-Net in Base 16 — Upper bound on s

There is no (21, 110, 1082)-net in base 16, because

1 times m-reduction [i] would yield (21, 109, 1082)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 179404 318061 901720 088563 689969 971216 913615 692614 703878 635866 175315 643961 630453 430593 458719 500900 520522 019007 436631 581794 244222 619796 > 16¹⁰⁹ [i]