MinT - Best Known (20, 20+69, s)-Nets in Base 16

Best Known (20, 20+69, s)-Nets in Base 16

(20, 20+69, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 89, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 89, 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+69, 129)-Net over F₁₆ — Digital

Digital (20, 89, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 89, 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+69, 1161)-Net in Base 16 — Upper bound on s

There is no (20, 89, 1162)-net in base 16, because

1 times m-reduction [i] would yield (20, 88, 1162)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9323 716391 967362 466086 033197 284342 785892 429697 298252 278910 584912 232606 385677 925776 554544 208400 859631 485296 > 16⁸⁸ [i]