MinT - Best Known (30, 30+111, s)-Nets in Base 8

Best Known (30, 30+111, s)-Nets in Base 8

(30, 30+111, 65)-Net over F₈ — Constructive and digital

Digital (30, 141, 65)-net over F₈, using

t-expansion [i] based on digital (14, 141, 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+111, 97)-Net over F₈ — Digital

Digital (30, 141, 97)-net over F₈, using

t-expansion [i] based on digital (28, 141, 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+111, 572)-Net in Base 8 — Upper bound on s

There is no (30, 141, 573)-net in base 8, because

1 times m-reduction [i] would yield (30, 140, 573)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 900681 203311 430390 564000 916982 170880 718637 123629 166385 305354 330326 488972 768186 862609 825091 452478 687237 947282 426186 272860 933272 > 8¹⁴⁰ [i]