MinT - Best Known (77, 166, s)-Nets in Base 8

Best Known (77, 166, s)-Nets in Base 8

(77, 166, 130)-Net over F₈ — Constructive and digital

Digital (77, 166, 130)-net over F₈, using

t-expansion [i] based on digital (76, 166, 130)-net over F₈, using
- 6 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)

(77, 166, 201)-Net over F₈ — Digital

Digital (77, 166, 201)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 166, 5975)-Net in Base 8 — Upper bound on s

There is no (77, 166, 5976)-net in base 8, because

1 times m-reduction [i] would yield (77, 165, 5976)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102399 560450 759439 464338 464612 326057 229467 428818 247239 980018 435082 677752 374122 756309 896452 521865 676488 180719 309686 716363 977220 797538 361001 329013 189492 > 8¹⁶⁵ [i]