MinT - Best Known (160−47, 160, s)-Nets in Base 8

Best Known (160−47, 160, s)-Nets in Base 8

(160−47, 160, 1026)-Net over F₈ — Constructive and digital

Digital (113, 160, 1026)-net over F₈, using

10 times m-reduction [i] based on digital (113, 170, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 85, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(160−47, 160, 3582)-Net over F₈ — Digital

Digital (113, 160, 3582)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−47, 160, 2357523)-Net in Base 8 — Upper bound on s

There is no (113, 160, 2357524)-net in base 8, because

1 times m-reduction [i] would yield (113, 159, 2357524)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390222 080595 657659 923918 596639 553320 746622 978127 674424 311439 651028 286281 295139 264359 885422 571290 595823 465291 719271 029395 689955 838113 540254 562240 > 8¹⁵⁹ [i]