MinT - Best Known (148−93, 148, s)-Nets in Base 8

Best Known (148−93, 148, s)-Nets in Base 8

(148−93, 148, 98)-Net over F₈ — Constructive and digital

Digital (55, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(148−93, 148, 144)-Net over F₈ — Digital

Digital (55, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 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]

(148−93, 148, 1948)-Net in Base 8 — Upper bound on s

There is no (55, 148, 1949)-net in base 8, because

1 times m-reduction [i] would yield (55, 147, 1949)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 751300 390552 130656 602577 889952 570934 511332 182022 819015 651404 813105 777528 202711 824391 933047 282620 817183 195339 879506 027642 468721 757408 > 8¹⁴⁷ [i]