MinT - Best Known (20, 20+56, s)-Nets in Base 16

Best Known (20, 20+56, s)-Nets in Base 16

(20, 20+56, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 76, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 76, 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]

(20, 20+56, 129)-Net over F₁₆ — Digital

Digital (20, 76, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 76, 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]

(20, 20+56, 1381)-Net in Base 16 — Upper bound on s

There is no (20, 76, 1382)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 32 714148 724733 660102 457400 934718 066925 132102 490752 722625 788452 373956 982784 018609 455088 754716 > 16⁷⁶ [i]