MinT - Best Known (148−58, 148, s)-Nets in Base 8

Best Known (148−58, 148, s)-Nets in Base 8

(148−58, 148, 354)-Net over F₈ — Constructive and digital

Digital (90, 148, 354)-net over F₈, using

18 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(148−58, 148, 432)-Net in Base 8 — Constructive

(90, 148, 432)-net in base 8, using

trace code for nets [i] based on (16, 74, 216)-net in base 64, using
- 3 times m-reduction [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(148−58, 148, 698)-Net over F₈ — Digital

Digital (90, 148, 698)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−58, 148, 67729)-Net in Base 8 — Upper bound on s

There is no (90, 148, 67730)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 428511 456253 601490 446049 470272 716414 274422 543272 264006 233674 279248 298143 856281 570389 496373 652999 512807 679686 697621 037219 796433 441696 > 8¹⁴⁸ [i]