MinT - Best Known (97, 97+55, s)-Nets in Base 8

Best Known (97, 97+55, s)-Nets in Base 8

(97, 97+55, 368)-Net over F₈ — Constructive and digital

Digital (97, 152, 368)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 28, 14)-net over F₈, using
  - net from sequence [i] based on digital (1, 13)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. digital (69, 124, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 62, 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+55, 576)-Net in Base 8 — Constructive

(97, 152, 576)-net in base 8, using

2 times m-reduction [i] based on (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+55, 1070)-Net over F₈ — Digital

Digital (97, 152, 1070)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+55, 175340)-Net in Base 8 — Upper bound on s

There is no (97, 152, 175341)-net in base 8, because

1 times m-reduction [i] would yield (97, 151, 175341)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23261 914789 456760 181500 145535 581236 902154 512952 031460 058400 455083 940742 851780 940795 335418 380928 793826 712661 860613 598766 026728 830716 043256 > 8¹⁵¹ [i]