MinT - Best Known (150−119, 150, s)-Nets in Base 8

Best Known (150−119, 150, s)-Nets in Base 8

(150−119, 150, 65)-Net over F₈ — Constructive and digital

Digital (31, 150, 65)-net over F₈, using

t-expansion [i] based on digital (14, 150, 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]

(150−119, 150, 97)-Net over F₈ — Digital

Digital (31, 150, 97)-net over F₈, using

t-expansion [i] based on digital (28, 150, 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]

(150−119, 150, 585)-Net in Base 8 — Upper bound on s

There is no (31, 150, 586)-net in base 8, because

1 times m-reduction [i] would yield (31, 149, 586)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 383 567718 722082 163592 774949 792504 630960 101570 118435 384615 766368 229970 762143 045235 263014 798186 609441 728313 782471 605083 560438 618512 014944 > 8¹⁴⁹ [i]