MinT - Best Known (82, 82+78, s)-Nets in Base 8

Best Known (82, 82+78, s)-Nets in Base 8

(82, 82+78, 160)-Net over F₈ — Constructive and digital

Digital (82, 160, 160)-net over F₈, using

2 times m-reduction [i] based on digital (82, 162, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 81, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(82, 82+78, 225)-Net in Base 8 — Constructive

(82, 160, 225)-net in base 8, using

8 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+78, 286)-Net over F₈ — Digital

Digital (82, 160, 286)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+78, 11126)-Net in Base 8 — Upper bound on s

There is no (82, 160, 11127)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 128384 697772 670853 031363 974327 331946 380963 481386 862237 093740 362853 459101 647896 046030 220373 737719 904206 476898 339244 954556 424238 266412 637662 234024 > 8¹⁶⁰ [i]