MinT - Best Known (111, 111+42, s)-Nets in Base 8

Best Known (111, 111+42, s)-Nets in Base 8

(111, 111+42, 1026)-Net over F₈ — Constructive and digital

Digital (111, 153, 1026)-net over F₈, using

13 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+42, 5426)-Net over F₈ — Digital

Digital (111, 153, 5426)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+42, 4710304)-Net in Base 8 — Upper bound on s

There is no (111, 153, 4710305)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 488571 552964 091759 614237 647210 491189 282266 585823 634159 669111 750168 020652 677779 028713 487604 562318 829401 405041 813879 009931 512135 200575 922656 > 8¹⁵³ [i]