MinT - Best Known (148−54, 148, s)-Nets in Base 8

Best Known (148−54, 148, s)-Nets in Base 8

(148−54, 148, 354)-Net over F₈ — Constructive and digital

Digital (94, 148, 354)-net over F₈, using

t-expansion [i] based on digital (93, 148, 354)-net over F₈, using
- 24 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(148−54, 148, 576)-Net in Base 8 — Constructive

(94, 148, 576)-net in base 8, using

trace code for nets [i] based on (20, 74, 288)-net in base 64, using
- 3 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]

(148−54, 148, 1003)-Net over F₈ — Digital

Digital (94, 148, 1003)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−54, 148, 139164)-Net in Base 8 — Upper bound on s

There is no (94, 148, 139165)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 435485 011399 462815 751576 080574 024230 065878 170104 679103 338082 234211 209344 327868 223629 328236 012732 531457 899911 450782 930077 930087 934420 > 8¹⁴⁸ [i]