MinT - Best Known (156−58, 156, s)-Nets in Base 8

Best Known (156−58, 156, s)-Nets in Base 8

(156−58, 156, 354)-Net over F₈ — Constructive and digital

Digital (98, 156, 354)-net over F₈, using

t-expansion [i] based on digital (93, 156, 354)-net over F₈, using
- 16 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(156−58, 156, 514)-Net in Base 8 — Constructive

(98, 156, 514)-net in base 8, using

base change [i] based on digital (59, 117, 514)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (59, 118, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 59, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]

(156−58, 156, 949)-Net over F₈ — Digital

Digital (98, 156, 949)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−58, 156, 120215)-Net in Base 8 — Upper bound on s

There is no (98, 156, 120216)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 273444 350294 970224 073623 358160 890996 193067 929729 671667 017182 662826 765578 690717 193363 481419 944716 111218 996575 346399 710787 048745 895519 915184 > 8¹⁵⁶ [i]