MinT - Best Known (21, 21+80, s)-Nets in Base 16

Best Known (21, 21+80, s)-Nets in Base 16

(21, 21+80, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 101, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 101, 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+80, 129)-Net over F₁₆ — Digital

Digital (21, 101, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 101, 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+80, 1131)-Net in Base 16 — Upper bound on s

There is no (21, 101, 1132)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 41 798705 816315 547805 303728 307588 764282 781018 337903 375632 690716 972273 118977 100412 177790 726459 596295 909748 069745 075310 504451 > 16¹⁰¹ [i]