MinT - Best Known (21, 21+72, s)-Nets in Base 16

Best Known (21, 21+72, s)-Nets in Base 16

(21, 21+72, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 93, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 93, 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]

(21, 21+72, 129)-Net over F₁₆ — Digital

Digital (21, 93, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 93, 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]

(21, 21+72, 1208)-Net in Base 16 — Upper bound on s

There is no (21, 93, 1209)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9779 756321 964260 850854 408749 141939 950038 855199 379090 039130 747147 823404 409401 804319 760234 849471 168346 310374 653486 > 16⁹³ [i]