MinT - Best Known (135−61, 135, s)-Nets in Base 8

Best Known (135−61, 135, s)-Nets in Base 8

(135−61, 135, 256)-Net over F₈ — Constructive and digital

Digital (74, 135, 256)-net over F₈, using

3 times m-reduction [i] based on digital (74, 138, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 69, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(135−61, 135, 340)-Net over F₈ — Digital

Digital (74, 135, 340)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−61, 135, 18580)-Net in Base 8 — Upper bound on s

There is no (74, 135, 18581)-net in base 8, because

1 times m-reduction [i] would yield (74, 134, 18581)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 339874 456426 737934 432517 052224 383904 667651 259363 790660 387044 717837 302168 394691 937680 345040 423206 591882 106018 111589 977920 > 8¹³⁴ [i]