MinT - Best Known (35, 35+61, s)-Nets in Base 16

Best Known (35, 35+61, s)-Nets in Base 16

(35, 35+61, 71)-Net over F₁₆ — Constructive and digital

Digital (35, 96, 71)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 32, 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, 64, 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]

(35, 35+61, 120)-Net in Base 16 — Constructive

(35, 96, 120)-net in base 16, using

24 times m-reduction [i] based on (35, 120, 120)-net in base 16, using
- base change [i] based on digital (11, 96, 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]

(35, 35+61, 193)-Net over F₁₆ — Digital

Digital (35, 96, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 96, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(35, 35+61, 5204)-Net in Base 16 — Upper bound on s

There is no (35, 96, 5205)-net in base 16, because

1 times m-reduction [i] would yield (35, 95, 5205)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 471175 069717 845920 284944 008168 210042 350036 048548 617345 231139 268004 733261 930765 443423 034620 891417 269685 986666 585376 > 16⁹⁵ [i]