MinT - Best Known (56, 56+51, s)-Nets in Base 8

Best Known (56, 56+51, s)-Nets in Base 8

(56, 56+51, 160)-Net over F₈ — Constructive and digital

Digital (56, 107, 160)-net over F₈, using

3 times m-reduction [i] based on digital (56, 110, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 55, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(56, 56+51, 224)-Net over F₈ — Digital

Digital (56, 107, 224)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+51, 9793)-Net in Base 8 — Upper bound on s

There is no (56, 107, 9794)-net in base 8, because

1 times m-reduction [i] would yield (56, 106, 9794)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534623 092224 970065 131551 657891 734290 621523 612272 254853 054719 698452 108424 614302 485780 895650 202680 > 8¹⁰⁶ [i]