MinT - Best Known (167−77, 167, s)-Nets in Base 8

Best Known (167−77, 167, s)-Nets in Base 8

(167−77, 167, 256)-Net over F₈ — Constructive and digital

Digital (90, 167, 256)-net over F₈, using

3 times m-reduction [i] based on digital (90, 170, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 85, 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]

(167−77, 167, 375)-Net over F₈ — Digital

Digital (90, 167, 375)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−77, 167, 18890)-Net in Base 8 — Upper bound on s

There is no (90, 167, 18891)-net in base 8, because

1 times m-reduction [i] would yield (90, 166, 18891)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 819928 156168 299770 895797 415200 943113 449491 924242 932711 457675 030519 387499 827379 158872 687533 271045 671938 167166 586890 505246 337436 620059 532097 368667 119092 > 8¹⁶⁶ [i]