MinT - Best Known (26, 26+42, s)-Nets in Base 16

Best Known (26, 26+42, s)-Nets in Base 16

(26, 26+42, 71)-Net over F₁₆ — Constructive and digital

Digital (26, 68, 71)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 23, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. digital (3, 45, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(26, 26+42, 120)-Net in Base 16 — Constructive

(26, 68, 120)-net in base 16, using

7 times m-reduction [i] based on (26, 75, 120)-net in base 16, using
- base change [i] based on digital (11, 60, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(26, 26+42, 150)-Net over F₁₆ — Digital

Digital (26, 68, 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+42, 4574)-Net in Base 16 — Upper bound on s

There is no (26, 68, 4575)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7593 965491 509446 454725 364582 181370 820487 674592 216556 437348 346113 946770 911611 603626 > 16⁶⁸ [i]