MinT - Best Known (21, 21+98, s)-Nets in Base 16

Best Known (21, 21+98, s)-Nets in Base 16

(21, 21+98, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 119, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 119, 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+98, 129)-Net over F₁₆ — Digital

Digital (21, 119, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 119, 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+98, 1043)-Net in Base 16 — Upper bound on s

There is no (21, 119, 1044)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 202287 068814 887839 279873 630551 992446 263173 595880 268998 015010 429306 386529 999366 450221 492887 656902 966306 436209 620329 275060 388091 836734 478340 973216 > 16¹¹⁹ [i]