MinT - Best Known (20, 20+74, s)-Nets in Base 16

Best Known (20, 20+74, s)-Nets in Base 16

(20, 20+74, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 94, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 94, 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]

(20, 20+74, 129)-Net over F₁₆ — Digital

Digital (20, 94, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 94, 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]

(20, 20+74, 1098)-Net in Base 16 — Upper bound on s

There is no (20, 94, 1099)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 154426 432481 418770 166268 615601 432259 446307 576380 111744 595372 626902 243340 885193 529955 130153 335914 463686 038334 348696 > 16⁹⁴ [i]