MinT - Best Known (95, 95+48, s)-Nets in Base 8

Best Known (95, 95+48, s)-Nets in Base 8

(95, 95+48, 399)-Net over F₈ — Constructive and digital

Digital (95, 143, 399)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (62, 110, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 55, 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]

(95, 95+48, 576)-Net in Base 8 — Constructive

(95, 143, 576)-net in base 8, using

7 times m-reduction [i] based on (95, 150, 576)-net in base 8, using
- trace code for nets [i] based on (20, 75, 288)-net in base 64, using
  - 2 times m-reduction [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]

(95, 95+48, 1491)-Net over F₈ — Digital

Digital (95, 143, 1491)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 95+48, 336632)-Net in Base 8 — Upper bound on s

There is no (95, 143, 336633)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1386 340788 606219 719985 473338 462004 767104 917774 858935 094812 948655 693819 822425 518266 924102 039335 943999 138449 358820 597342 148607 885303 > 8¹⁴³ [i]