MinT - Best Known (160−68, 160, s)-Nets in Base 8

Best Known (160−68, 160, s)-Nets in Base 8

(160−68, 160, 354)-Net over F₈ — Constructive and digital

Digital (92, 160, 354)-net over F₈, using

10 times m-reduction [i] based on digital (92, 170, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 85, 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]

(160−68, 160, 514)-Net over F₈ — Digital

Digital (92, 160, 514)-net over F₈, using

trace code for nets [i] based on digital (12, 80, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(160−68, 160, 34351)-Net in Base 8 — Upper bound on s

There is no (92, 160, 34352)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 124016 551386 097522 208938 787432 016716 287187 962055 481416 807329 407405 936925 105664 148477 714450 870622 725489 658518 893434 713860 501905 173546 152926 227981 > 8¹⁶⁰ [i]