MinT - Best Known (88, 88+71, s)-Nets in Base 8

Best Known (88, 88+71, s)-Nets in Base 8

(88, 88+71, 354)-Net over F₈ — Constructive and digital

Digital (88, 159, 354)-net over F₈, using

3 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(88, 88+71, 411)-Net over F₈ — Digital

Digital (88, 159, 411)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+71, 23690)-Net in Base 8 — Upper bound on s

There is no (88, 159, 23691)-net in base 8, because

1 times m-reduction [i] would yield (88, 158, 23691)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48833 999525 188391 935706 633249 948341 269535 929423 094567 502646 806452 810648 487543 046278 007045 028870 764997 211749 893065 980943 835310 073023 223616 434304 > 8¹⁵⁸ [i]