MinT - Best Known (83−58, 83, s)-Nets in Base 16

Best Known (83−58, 83, s)-Nets in Base 16

(83−58, 83, 65)-Net over F₁₆ — Constructive and digital

Digital (25, 83, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 83, 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]

(83−58, 83, 98)-Net in Base 16 — Constructive

(25, 83, 98)-net in base 16, using

7 times m-reduction [i] based on (25, 90, 98)-net in base 16, using
- base change [i] based on digital (7, 72, 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]

(83−58, 83, 144)-Net over F₁₆ — Digital

Digital (25, 83, 144)-net over F₁₆, using

net from sequence [i] based on digital (25, 143)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 25 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(83−58, 83, 2158)-Net in Base 16 — Upper bound on s

There is no (25, 83, 2159)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8828 166634 605484 923370 557035 617505 644532 530073 790003 439047 404976 950800 514732 509148 522722 668217 869916 > 16⁸³ [i]