MinT - Best Known (115, 115+44, s)-Nets in Base 8

Best Known (115, 115+44, s)-Nets in Base 8

(115, 115+44, 1026)-Net over F₈ — Constructive and digital

Digital (115, 159, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 159, 1026)-net over F₈, using
- 13 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(115, 115+44, 5290)-Net over F₈ — Digital

Digital (115, 159, 5290)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+44, 4351422)-Net in Base 8 — Upper bound on s

There is no (115, 159, 4351423)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390219 446029 431088 314141 047285 403495 977824 307277 762966 361750 990513 178430 561311 014445 545020 499287 132889 660266 199052 136073 963838 073841 015444 728747 > 8¹⁵⁹ [i]