MinT - Best Known (111, 161, s)-Nets in Base 8

Best Known (111, 161, s)-Nets in Base 8

(111, 161, 1026)-Net over F₈ — Constructive and digital

Digital (111, 161, 1026)-net over F₈, using

5 times m-reduction [i] based on digital (111, 166, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 83, 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]

(111, 161, 2557)-Net over F₈ — Digital

Digital (111, 161, 2557)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 161, 951524)-Net in Base 8 — Upper bound on s

There is no (111, 161, 951525)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 973998 320904 492343 790501 071351 602483 103194 936294 541269 770339 961563 777264 387079 516939 437826 453592 291489 802324 851352 480132 664574 750934 942693 144528 > 8¹⁶¹ [i]