MinT - Best Known (152−52, 152, s)-Nets in Base 8

Best Known (152−52, 152, s)-Nets in Base 8

(152−52, 152, 389)-Net over F₈ — Constructive and digital

Digital (100, 152, 389)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 34, 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 (66, 118, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 59, 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]

(152−52, 152, 576)-Net in Base 8 — Constructive

(100, 152, 576)-net in base 8, using

6 times m-reduction [i] based on (100, 158, 576)-net in base 8, using
- trace code for nets [i] based on (21, 79, 288)-net in base 64, using
  - 5 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
    - base change [i] based on digital (9, 72, 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]

(152−52, 152, 1420)-Net over F₈ — Digital

Digital (100, 152, 1420)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−52, 152, 286928)-Net in Base 8 — Upper bound on s

There is no (100, 152, 286929)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186081 687677 571031 481170 775748 053488 488680 346017 454138 869698 059305 640879 313386 759341 413872 662509 895093 151057 760413 370372 059232 103258 732128 > 8¹⁵² [i]