MinT - Best Known (77, 77+69, s)-Nets in Base 8

Best Known (77, 77+69, s)-Nets in Base 8

(77, 77+69, 208)-Net over F₈ — Constructive and digital

Digital (77, 146, 208)-net over F₈, using

2 times m-reduction [i] based on 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, 77+69, 225)-Net in Base 8 — Constructive

(77, 146, 225)-net in base 8, using

2 times m-reduction [i] based on (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, 77+69, 301)-Net over F₈ — Digital

Digital (77, 146, 301)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+69, 13712)-Net in Base 8 — Upper bound on s

There is no (77, 146, 13713)-net in base 8, because

1 times m-reduction [i] would yield (77, 145, 13713)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88846 692569 941453 862813 904378 238278 416059 327464 548603 944238 352744 994184 842539 205270 561431 631973 919427 299570 316093 990690 876276 514272 > 8¹⁴⁵ [i]