MinT - Best Known (22, 22+108, s)-Nets in Base 16

Best Known (22, 22+108, s)-Nets in Base 16

(22, 22+108, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 130, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 130, 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+108, 129)-Net over F₁₆ — Digital

Digital (22, 130, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 130, 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+108, 1077)-Net in Base 16 — Upper bound on s

There is no (22, 130, 1078)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 537062 179961 870346 090910 517269 983961 241759 819501 226892 323790 145996 866202 856097 915008 232425 609278 794430 264980 295716 901872 856143 733980 616377 004924 087707 850656 > 16¹³⁰ [i]