MinT - Best Known (22, 22+71, s)-Nets in Base 16

Best Known (22, 22+71, s)-Nets in Base 16

(22, 22+71, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 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]

(22, 22+71, 129)-Net over F₁₆ — Digital

Digital (22, 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]

(22, 22+71, 1336)-Net in Base 16 — Upper bound on s

There is no (22, 93, 1337)-net in base 16, because

1 times m-reduction [i] would yield (22, 92, 1337)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 603 974727 474441 690296 405404 224607 148356 733253 402264 806883 254836 777943 959925 797365 114199 972344 271288 805687 639176 > 16⁹² [i]