MinT - Best Known (53, 53+95, s)-Nets in Base 8

Best Known (53, 53+95, s)-Nets in Base 8

(53, 53+95, 98)-Net over F₈ — Constructive and digital

Digital (53, 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]

(53, 53+95, 144)-Net over F₈ — Digital

Digital (53, 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]

(53, 53+95, 1722)-Net in Base 8 — Upper bound on s

There is no (53, 148, 1723)-net in base 8, because

1 times m-reduction [i] would yield (53, 147, 1723)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 748993 047700 041750 369613 482424 885356 912327 765036 514831 551778 091210 120443 142028 009898 363759 084639 621198 411492 712649 696856 323263 191728 > 8¹⁴⁷ [i]