MinT - Best Known (97, 97+57, s)-Nets in Base 8

Best Known (97, 97+57, s)-Nets in Base 8

(97, 97+57, 354)-Net over F₈ — Constructive and digital

Digital (97, 154, 354)-net over F₈, using

t-expansion [i] based on digital (93, 154, 354)-net over F₈, using
- 18 times m-reduction [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]

(97, 97+57, 576)-Net in Base 8 — Constructive

(97, 154, 576)-net in base 8, using

trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(97, 97+57, 961)-Net over F₈ — Digital

Digital (97, 154, 961)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+57, 138865)-Net in Base 8 — Upper bound on s

There is no (97, 154, 138866)-net in base 8, because

1 times m-reduction [i] would yield (97, 153, 138866)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 488752 527705 303838 263538 973474 690776 187321 538711 550652 637455 227977 196119 197280 864316 031813 913945 854847 567510 236252 967524 577225 532526 574392 > 8¹⁵³ [i]