MinT - Best Known (164−69, 164, s)-Nets in Base 8

Best Known (164−69, 164, s)-Nets in Base 8

(164−69, 164, 354)-Net over F₈ — Constructive and digital

Digital (95, 164, 354)-net over F₈, using

t-expansion [i] based on digital (93, 164, 354)-net over F₈, using
- 8 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]

(164−69, 164, 546)-Net over F₈ — Digital

Digital (95, 164, 546)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−69, 164, 41273)-Net in Base 8 — Upper bound on s

There is no (95, 164, 41274)-net in base 8, because

1 times m-reduction [i] would yield (95, 163, 41274)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1598 855615 594314 691563 037056 939300 281433 695891 163935 362896 359578 573048 517260 210571 429658 013157 534228 155015 560271 001309 439871 178359 008654 313486 721684 > 8¹⁶³ [i]