MinT - Best Known (158−85, 158, s)-Nets in Base 8

Best Known (158−85, 158, s)-Nets in Base 8

(158−85, 158, 130)-Net over F₈ — Constructive and digital

Digital (73, 158, 130)-net over F₈, using

5 times m-reduction [i] based on digital (73, 163, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 59, 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, 104, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(158−85, 158, 190)-Net over F₈ — Digital

Digital (73, 158, 190)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−85, 158, 193)-Net in Base 8

(73, 158, 193)-net in base 8, using

2 times m-reduction [i] based on (73, 160, 193)-net in base 8, using
- base change [i] based on digital (33, 120, 193)-net over F₁₆, using
  - net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
      - a curve from the manYPoints database [i]

(158−85, 158, 5578)-Net in Base 8 — Upper bound on s

There is no (73, 158, 5579)-net in base 8, because

1 times m-reduction [i] would yield (73, 157, 5579)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6139 294368 653418 785192 801958 080192 602201 706930 325171 379604 703989 246926 544840 298903 078930 796456 807008 982100 376887 739659 425943 989028 815460 744466 > 8¹⁵⁷ [i]