MinT - Best Known (21, 21+76, s)-Nets in Base 16

Best Known (21, 21+76, s)-Nets in Base 16

(21, 21+76, 65)-Net over F₁₆ — Constructive and digital

Digital (21, 97, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 97, 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+76, 129)-Net over F₁₆ — Digital

Digital (21, 97, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 97, 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+76, 1165)-Net in Base 16 — Upper bound on s

There is no (21, 97, 1166)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 632 783103 209899 946742 050061 566511 608711 518244 949154 761257 584559 702513 324986 582746 198101 588492 601773 041396 094563 397296 > 16⁹⁷ [i]