MinT - Best Known (159−76, 159, s)-Nets in Base 8

Best Known (159−76, 159, s)-Nets in Base 8

(159−76, 159, 208)-Net over F₈ — Constructive and digital

Digital (83, 159, 208)-net over F₈, using

1 times m-reduction [i] based on digital (83, 160, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 80, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(159−76, 159, 225)-Net in Base 8 — Constructive

(83, 159, 225)-net in base 8, using

13 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
- base change [i] based on digital (40, 129, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(159−76, 159, 309)-Net over F₈ — Digital

Digital (83, 159, 309)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−76, 159, 12871)-Net in Base 8 — Upper bound on s

There is no (83, 159, 12872)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 391189 536031 221149 342539 157395 768447 951340 478959 300359 227452 882721 731348 567513 035640 993036 775390 294310 774413 683236 610962 480962 753588 561277 950026 > 8¹⁵⁹ [i]