MinT - Best Known (148−87, 148, s)-Nets in Base 8

Best Known (148−87, 148, s)-Nets in Base 8

(148−87, 148, 98)-Net over F₈ — Constructive and digital

Digital (61, 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]

(148−87, 148, 144)-Net over F₈ — Digital

Digital (61, 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]

(148−87, 148, 2921)-Net in Base 8 — Upper bound on s

There is no (61, 148, 2922)-net in base 8, because

1 times m-reduction [i] would yield (61, 147, 2922)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 682099 939702 121687 844788 739324 843821 559043 102514 013721 172279 545843 855153 787467 201601 184537 488310 839578 004401 871316 342979 990903 893600 > 8¹⁴⁷ [i]