MinT - Best Known (160−56, 160, s)-Nets in Base 8

Best Known (160−56, 160, s)-Nets in Base 8

(160−56, 160, 382)-Net over F₈ — Constructive and digital

Digital (104, 160, 382)-net over F₈, using

1 times m-reduction [i] based on digital (104, 161, 382)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 33, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]
  2. digital (71, 128, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 64, 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]

(160−56, 160, 576)-Net in Base 8 — Constructive

(104, 160, 576)-net in base 8, using

6 times m-reduction [i] based on (104, 166, 576)-net in base 8, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
  - 1 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]

(160−56, 160, 1319)-Net over F₈ — Digital

Digital (104, 160, 1319)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−56, 160, 233554)-Net in Base 8 — Upper bound on s

There is no (104, 160, 233555)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 121850 728311 386173 739173 196405 704029 439493 778671 473706 690954 323537 163666 889819 091484 115504 643654 975509 176053 891478 036902 312528 573008 142178 682192 > 8¹⁶⁰ [i]