MinT - Best Known (30, 30+123, s)-Nets in Base 8

Best Known (30, 30+123, s)-Nets in Base 8

(30, 30+123, 65)-Net over F₈ — Constructive and digital

Digital (30, 153, 65)-net over F₈, using

t-expansion [i] based on digital (14, 153, 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]

(30, 30+123, 97)-Net over F₈ — Digital

Digital (30, 153, 97)-net over F₈, using

t-expansion [i] based on digital (28, 153, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(30, 30+123, 561)-Net in Base 8 — Upper bound on s

There is no (30, 153, 562)-net in base 8, because

1 times m-reduction [i] would yield (30, 152, 562)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 204984 957154 617452 631203 925450 149500 366661 504362 186374 883777 106244 203614 068019 680949 784282 134603 458271 611149 625738 430961 826461 907210 693760 > 8¹⁵² [i]