MinT - Best Known (170−79, 170, s)-Nets in Base 8

Best Known (170−79, 170, s)-Nets in Base 8

(170−79, 170, 256)-Net over F₈ — Constructive and digital

Digital (91, 170, 256)-net over F₈, using

2 times m-reduction [i] based on digital (91, 172, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 86, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(170−79, 170, 368)-Net over F₈ — Digital

Digital (91, 170, 368)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−79, 170, 17993)-Net in Base 8 — Upper bound on s

There is no (91, 170, 17994)-net in base 8, because

1 times m-reduction [i] would yield (91, 169, 17994)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 104908 165920 037243 421160 243655 766297 378020 445931 282669 340870 280540 026962 830904 643158 091410 729315 883246 396956 883877 820756 985515 380587 454618 823236 782696 > 8¹⁶⁹ [i]