MinT - Best Known (131−56, 131, s)-Nets in Base 8

Best Known (131−56, 131, s)-Nets in Base 8

(131−56, 131, 354)-Net over F₈ — Constructive and digital

Digital (75, 131, 354)-net over F₈, using

5 times m-reduction [i] based on digital (75, 136, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 68, 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]

(131−56, 131, 421)-Net over F₈ — Digital

Digital (75, 131, 421)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−56, 131, 27089)-Net in Base 8 — Upper bound on s

There is no (75, 131, 27090)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20188 674118 331599 049696 968522 010875 586634 159319 831439 992136 353446 239730 471619 222268 759280 138213 042515 508925 663439 383824 > 8¹³¹ [i]