MinT - Best Known (76, 155, s)-Nets in Base 8

Best Known (76, 155, s)-Nets in Base 8

(76, 155, 130)-Net over F₈ — Constructive and digital

Digital (76, 155, 130)-net over F₈, using

17 times m-reduction [i] based on digital (76, 172, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 62, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (14, 110, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(76, 155, 232)-Net over F₈ — Digital

Digital (76, 155, 232)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 155, 8073)-Net in Base 8 — Upper bound on s

There is no (76, 155, 8074)-net in base 8, because

1 times m-reduction [i] would yield (76, 154, 8074)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 943158 851172 415608 895147 771759 655575 040194 088646 366733 972299 691160 818388 594036 161477 870090 020270 968264 435938 319629 640098 560060 968183 985776 > 8¹⁵⁴ [i]