MinT - Best Known (111, 111+40, s)-Nets in Base 8

Best Known (111, 111+40, s)-Nets in Base 8

(111, 111+40, 1026)-Net over F₈ — Constructive and digital

Digital (111, 151, 1026)-net over F₈, using

15 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, 111+40, 6920)-Net over F₈ — Digital

Digital (111, 151, 6920)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+40, 7807947)-Net in Base 8 — Upper bound on s

There is no (111, 151, 7807948)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23258 846706 851738 849817 756162 914339 587282 080768 566211 935255 187586 858197 303724 754429 638425 280698 254163 423546 162377 990580 538385 311612 681576 > 8¹⁵¹ [i]