MinT - Best Known (135−65, 135, s)-Nets in Base 8

Best Known (135−65, 135, s)-Nets in Base 8

(135−65, 135, 160)-Net over F₈ — Constructive and digital

Digital (70, 135, 160)-net over F₈, using

3 times m-reduction [i] based on digital (70, 138, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 69, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(135−65, 135, 261)-Net over F₈ — Digital

Digital (70, 135, 261)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−65, 135, 11032)-Net in Base 8 — Upper bound on s

There is no (70, 135, 11033)-net in base 8, because

1 times m-reduction [i] would yield (70, 134, 11033)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 337290 813029 171600 113239 637271 350560 112200 750065 233898 416898 139878 408156 212196 283591 165182 694025 892779 858101 828419 903640 > 8¹³⁴ [i]