MinT - Best Known (173−77, 173, s)-Nets in Base 8

Best Known (173−77, 173, s)-Nets in Base 8

(173−77, 173, 354)-Net over F₈ — Constructive and digital

Digital (96, 173, 354)-net over F₈, using

8¹ times duplication [i] based on digital (95, 172, 354)-net over F₈, using
- t-expansion [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(173−77, 173, 449)-Net over F₈ — Digital

Digital (96, 173, 449)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−77, 173, 26240)-Net in Base 8 — Upper bound on s

There is no (96, 173, 26241)-net in base 8, because

1 times m-reduction [i] would yield (96, 172, 26241)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214534 618543 860621 055818 162546 902319 975262 779679 866975 557221 824139 880705 160100 975051 755823 147467 308515 826113 631301 670815 613950 553763 207642 368489 005023 950144 > 8¹⁷² [i]