MinT - Best Known (72, 72+83, s)-Nets in Base 8

Best Known (72, 72+83, s)-Nets in Base 8

(72, 72+83, 130)-Net over F₈ — Constructive and digital

Digital (72, 155, 130)-net over F₈, using

5 times m-reduction [i] based on digital (72, 160, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 58, 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, 102, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(72, 72+83, 191)-Net over F₈ — Digital

Digital (72, 155, 191)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+83, 193)-Net in Base 8

(72, 155, 193)-net in base 8, using

1 times m-reduction [i] based on (72, 156, 193)-net in base 8, using
- base change [i] based on digital (33, 117, 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]

(72, 72+83, 5661)-Net in Base 8 — Upper bound on s

There is no (72, 155, 5662)-net in base 8, because

1 times m-reduction [i] would yield (72, 154, 5662)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 950184 213654 629459 510674 597418 451563 601760 428586 357675 475423 400259 032317 931499 884226 187220 742575 570112 562752 661910 870530 559815 018729 917200 > 8¹⁵⁴ [i]