MinT - Best Known (73, 73+87, s)-Nets in Base 8

Best Known (73, 73+87, s)-Nets in Base 8

(73, 73+87, 130)-Net over F₈ — Constructive and digital

Digital (73, 160, 130)-net over F₈, using

3 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)

(73, 73+87, 184)-Net over F₈ — Digital

Digital (73, 160, 184)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+87, 193)-Net in Base 8

(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]

(73, 73+87, 5241)-Net in Base 8 — Upper bound on s

There is no (73, 160, 5242)-net in base 8, because

1 times m-reduction [i] would yield (73, 159, 5242)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 391504 965257 740907 604843 700448 186752 369930 880278 503743 439939 912435 051652 301030 826198 986462 080666 692315 545181 391109 290974 410324 773191 854098 836200 > 8¹⁵⁹ [i]