MinT - Best Known (160−48, 160, s)-Nets in Base 8

Best Known (160−48, 160, s)-Nets in Base 8

(160−48, 160, 1026)-Net over F₈ — Constructive and digital

Digital (112, 160, 1026)-net over F₈, using

8 times m-reduction [i] based on digital (112, 168, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 84, 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]

(160−48, 160, 3138)-Net over F₈ — Digital

Digital (112, 160, 3138)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−48, 160, 1468453)-Net in Base 8 — Upper bound on s

There is no (112, 160, 1468454)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 121774 799338 458312 123202 825458 230943 126716 635362 441721 915529 846347 005800 543278 470198 938568 413286 112222 893322 904559 168386 855491 263310 648270 995428 > 8¹⁶⁰ [i]