MinT - Best Known (86, 160, s)-Nets in Base 8

Best Known (86, 160, s)-Nets in Base 8

(86, 160, 256)-Net over F₈ — Constructive and digital

Digital (86, 160, 256)-net over F₈, using

2 times m-reduction [i] based on digital (86, 162, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 81, 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]

(86, 160, 357)-Net over F₈ — Digital

Digital (86, 160, 357)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 160, 16806)-Net in Base 8 — Upper bound on s

There is no (86, 160, 16807)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 127996 749658 385906 443850 331704 072017 025480 685789 677074 107926 340790 549580 906840 857777 209263 638207 184029 993154 120518 265334 164145 973533 776387 113962 > 8¹⁶⁰ [i]