MinT - Best Known (147−71, 147, s)-Nets in Base 8

Best Known (147−71, 147, s)-Nets in Base 8

(147−71, 147, 160)-Net over F₈ — Constructive and digital

Digital (76, 147, 160)-net over F₈, using

3 times m-reduction [i] based on digital (76, 150, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 75, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(147−71, 147, 276)-Net over F₈ — Digital

Digital (76, 147, 276)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−71, 147, 11601)-Net in Base 8 — Upper bound on s

There is no (76, 147, 11602)-net in base 8, because

1 times m-reduction [i] would yield (76, 146, 11602)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 710604 813367 005062 190657 374335 621659 597497 287481 945385 989636 290020 261058 155185 670477 699636 282034 565096 164058 450260 054653 878403 899984 > 8¹⁴⁶ [i]