MinT - Best Known (22, 22+72, s)-Nets in Base 16

Best Known (22, 22+72, s)-Nets in Base 16

(22, 22+72, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 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]

(22, 22+72, 129)-Net over F₁₆ — Digital

Digital (22, 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]

(22, 22+72, 1306)-Net in Base 16 — Upper bound on s

There is no (22, 94, 1307)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 154900 180215 292427 968097 989379 642086 894604 278805 387029 433729 173128 459668 139655 092713 688731 808077 779218 626519 636656 > 16⁹⁴ [i]