MinT - Best Known (35, 77, s)-Nets in Base 16

Best Known (35, 77, s)-Nets in Base 16

(35, 77, 130)-Net over F₁₆ — Constructive and digital

Digital (35, 77, 130)-net over F₁₆, using

4 times m-reduction [i] based on digital (35, 81, 130)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (6, 29, 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]
  2. digital (6, 52, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆ (see above)

(35, 77, 177)-Net in Base 16 — Constructive

(35, 77, 177)-net in base 16, using

7 times m-reduction [i] based on (35, 84, 177)-net in base 16, using
- base change [i] based on digital (7, 56, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(35, 77, 193)-Net over F₁₆ — Digital

Digital (35, 77, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 77, 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, 77, 209)-Net in Base 16

(35, 77, 209)-net in base 16, using

1 times m-reduction [i] based on (35, 78, 209)-net in base 16, using
- base change [i] based on digital (9, 52, 209)-net over F₆₄, using
  - net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
      - a curve from the manYPoints database [i]

(35, 77, 15037)-Net in Base 16 — Upper bound on s

There is no (35, 77, 15038)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 521 763969 049259 781172 277158 045165 843108 634535 788314 761477 768176 491541 997013 930883 374574 961721 > 16⁷⁷ [i]