MinT - Best Known (22, 22+85, s)-Nets in Base 16

Best Known (22, 22+85, s)-Nets in Base 16

(22, 22+85, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 107, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 107, 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]

(22, 22+85, 129)-Net over F₁₆ — Digital

Digital (22, 107, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 107, 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]

(22, 22+85, 1180)-Net in Base 16 — Upper bound on s

There is no (22, 107, 1181)-net in base 16, because

1 times m-reduction [i] would yield (22, 106, 1181)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 383728 714082 789515 938704 308087 656202 452424 933591 202647 930797 894031 139535 992071 023648 665121 717499 326802 560129 930323 180257 127256 > 16¹⁰⁶ [i]