MinT - Best Known (136−62, 136, s)-Nets in Base 8

Best Known (136−62, 136, s)-Nets in Base 8

(136−62, 136, 256)-Net over F₈ — Constructive and digital

Digital (74, 136, 256)-net over F₈, using

2 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]

(136−62, 136, 329)-Net over F₈ — Digital

Digital (74, 136, 329)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−62, 136, 16231)-Net in Base 8 — Upper bound on s

There is no (74, 136, 16232)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 661 682136 535717 535117 307215 281003 965118 719185 620065 153417 239366 283021 112937 917894 550631 787506 867435 085323 155852 896653 533220 > 8¹³⁶ [i]