MinT - Best Known (22, 129, s)-Nets in Base 16

Best Known (22, 129, s)-Nets in Base 16

(22, 129, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 129, 65)-net over F₁₆, using

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

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

t-expansion [i] based on digital (19, 129, 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, 129, 1081)-Net in Base 16 — Upper bound on s

There is no (22, 129, 1082)-net in base 16, because

1 times m-reduction [i] would yield (22, 128, 1082)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13546 561735 187867 351100 714384 779062 613502 703948 219222 588181 485736 371055 888465 091669 523777 208957 873368 247014 464666 452866 709895 279865 293547 804459 219153 171966 > 16¹²⁸ [i]