MinT - Best Known (82, 82+74, s)-Nets in Base 8

Best Known (82, 82+74, s)-Nets in Base 8

(82, 82+74, 208)-Net over F₈ — Constructive and digital

Digital (82, 156, 208)-net over F₈, using

2 times m-reduction [i] based on digital (82, 158, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 79, 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]

(82, 82+74, 225)-Net in Base 8 — Constructive

(82, 156, 225)-net in base 8, using

12 times m-reduction [i] based on (82, 168, 225)-net in base 8, using
- base change [i] based on digital (40, 126, 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]

(82, 82+74, 314)-Net over F₈ — Digital

Digital (82, 156, 314)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+74, 13417)-Net in Base 8 — Upper bound on s

There is no (82, 156, 13418)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 405375 084474 887917 928225 395206 495327 763483 025821 259814 525132 800532 639796 182627 579141 989047 191203 875950 154479 595614 403934 814032 808514 702470 > 8¹⁵⁶ [i]