MinT - Best Known (100−39, 100, s)-Nets in Base 8

Best Known (100−39, 100, s)-Nets in Base 8

(100−39, 100, 354)-Net over F₈ — Constructive and digital

Digital (61, 100, 354)-net over F₈, using

8 times m-reduction [i] based on digital (61, 108, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 54, 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]

(100−39, 100, 384)-Net in Base 8 — Constructive

(61, 100, 384)-net in base 8, using

8² times duplication [i] based on (59, 98, 384)-net in base 8, using
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
  - base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(100−39, 100, 526)-Net over F₈ — Digital

Digital (61, 100, 526)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−39, 100, 57491)-Net in Base 8 — Upper bound on s

There is no (61, 100, 57492)-net in base 8, because

1 times m-reduction [i] would yield (61, 99, 57492)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 254677 211552 318159 834745 258593 928656 202444 453185 810152 056677 246687 331247 901376 959296 059655 > 8⁹⁹ [i]