MinT - Best Known (26, 26+68, s)-Nets in Base 16

Best Known (26, 26+68, s)-Nets in Base 16

(26, 26+68, 65)-Net over F₁₆ — Constructive and digital

Digital (26, 94, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 94, 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]

(26, 26+68, 98)-Net in Base 16 — Constructive

(26, 94, 98)-net in base 16, using

1 times m-reduction [i] based on (26, 95, 98)-net in base 16, using
- base change [i] based on digital (7, 76, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(26, 26+68, 150)-Net over F₁₆ — Digital

Digital (26, 94, 150)-net over F₁₆, using

net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
  - a curve from the manYPoints database [i]

(26, 26+68, 1906)-Net in Base 16 — Upper bound on s

There is no (26, 94, 1907)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 155995 957377 716024 442728 963706 953710 033048 566081 871513 929845 571951 687066 795654 565759 703979 264198 230769 300231 852121 > 16⁹⁴ [i]