MinT - Best Known (77, 148, s)-Nets in Base 8

Best Known (77, 148, s)-Nets in Base 8

(77, 148, 208)-Net over F₈ — Constructive and digital

Digital (77, 148, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 74, 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]

(77, 148, 225)-Net in Base 8 — Constructive

(77, 148, 225)-net in base 8, using

base change [i] based on digital (40, 111, 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]

(77, 148, 286)-Net over F₈ — Digital

Digital (77, 148, 286)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 148, 12313)-Net in Base 8 — Upper bound on s

There is no (77, 148, 12314)-net in base 8, because

1 times m-reduction [i] would yield (77, 147, 12314)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 692284 403625 569937 491677 742471 060439 796113 931396 960093 394383 324162 974251 477094 472028 545761 867543 009035 582792 957377 847485 128842 530304 > 8¹⁴⁷ [i]