MinT - Best Known (93−33, 93, s)-Nets in Base 8

Best Known (93−33, 93, s)-Nets in Base 8

(93−33, 93, 354)-Net over F₈ — Constructive and digital

Digital (60, 93, 354)-net over F₈, using

13 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 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]

(93−33, 93, 516)-Net in Base 8 — Constructive

(60, 93, 516)-net in base 8, using

1 times m-reduction [i] based on (60, 94, 516)-net in base 8, using
- trace code for nets [i] based on (13, 47, 258)-net in base 64, using
  - 1 times m-reduction [i] based on (13, 48, 258)-net in base 64, using
    - base change [i] based on digital (1, 36, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(93−33, 93, 786)-Net over F₈ — Digital

Digital (60, 93, 786)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−33, 93, 151418)-Net in Base 8 — Upper bound on s

There is no (60, 93, 151419)-net in base 8, because

1 times m-reduction [i] would yield (60, 92, 151419)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 121418 279432 671338 765055 945043 421163 368179 090084 174949 221152 915687 207457 101474 843445 > 8⁹² [i]