MinT - Best Known (153−57, 153, s)-Nets in Base 8

Best Known (153−57, 153, s)-Nets in Base 8

(153−57, 153, 354)-Net over F₈ — Constructive and digital

Digital (96, 153, 354)-net over F₈, using

t-expansion [i] based on digital (93, 153, 354)-net over F₈, using
- 19 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]

(153−57, 153, 514)-Net in Base 8 — Constructive

(96, 153, 514)-net in base 8, using

8¹ times duplication [i] based on (95, 152, 514)-net in base 8, using
- base change [i] based on digital (57, 114, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 57, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]

(153−57, 153, 924)-Net over F₈ — Digital

Digital (96, 153, 924)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−57, 153, 128924)-Net in Base 8 — Upper bound on s

There is no (96, 153, 128925)-net in base 8, because

1 times m-reduction [i] would yield (96, 152, 128925)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186077 835091 790679 775400 056155 940057 534618 081559 336853 847980 361275 668020 816388 460740 122419 324918 637270 623230 061386 518180 675019 215245 084825 > 8¹⁵² [i]