MinT - Best Known (90−68, 90, s)-Nets in Base 16

Best Known (90−68, 90, s)-Nets in Base 16

(90−68, 90, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 90, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 90, 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]

(90−68, 90, 129)-Net over F₁₆ — Digital

Digital (22, 90, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 90, 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]

(90−68, 90, 1370)-Net in Base 16 — Upper bound on s

There is no (22, 90, 1371)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 378439 837471 080109 142952 092673 665465 117210 986020 971094 094938 169706 994932 805695 612258 493273 317547 841176 398186 > 16⁹⁰ [i]