MinT - Best Known (145−87, 145, s)-Nets in Base 8

Best Known (145−87, 145, s)-Nets in Base 8

(145−87, 145, 98)-Net over F₈ — Constructive and digital

Digital (58, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(145−87, 145, 144)-Net over F₈ — Digital

Digital (58, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(145−87, 145, 2523)-Net in Base 8 — Upper bound on s

There is no (58, 145, 2524)-net in base 8, because

1 times m-reduction [i] would yield (58, 144, 2524)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11143 546248 813313 329987 223843 700431 846123 894026 812944 862381 157964 344251 769370 965755 706686 591010 439533 744056 233063 791383 811312 740550 > 8¹⁴⁴ [i]