MinT - Best Known (147−50, 147, s)-Nets in Base 8

Best Known (147−50, 147, s)-Nets in Base 8

(147−50, 147, 389)-Net over F₈ — Constructive and digital

Digital (97, 147, 389)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 33, 35)-net over F₈, using
  - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using a function field by SÃ©mirat [i]
2. digital (64, 114, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 57, 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]

(147−50, 147, 576)-Net in Base 8 — Constructive

(97, 147, 576)-net in base 8, using

7 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]

(147−50, 147, 1422)-Net over F₈ — Digital

Digital (97, 147, 1422)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−50, 147, 296943)-Net in Base 8 — Upper bound on s

There is no (97, 147, 296944)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 678563 759469 093432 965848 192383 895914 357842 648291 485429 204126 639289 869713 860111 254542 079659 852704 974936 994606 533969 629020 413739 185842 > 8¹⁴⁷ [i]