MinT - Best Known (153−65, 153, s)-Nets in Base 8

Best Known (153−65, 153, s)-Nets in Base 8

(153−65, 153, 354)-Net over F₈ — Constructive and digital

Digital (88, 153, 354)-net over F₈, using

9 times m-reduction [i] based on digital (88, 162, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 81, 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]

(153−65, 153, 493)-Net over F₈ — Digital

Digital (88, 153, 493)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−65, 153, 35580)-Net in Base 8 — Upper bound on s

There is no (88, 153, 35581)-net in base 8, because

1 times m-reduction [i] would yield (88, 152, 35581)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186115 424989 755799 127649 412164 874667 460201 318232 520369 284798 549617 237020 852137 675969 100506 242045 541977 406781 872911 889392 976350 844464 903945 > 8¹⁵² [i]