MinT - Best Known (55, 55+113, s)-Nets in Base 8

Best Known (55, 55+113, s)-Nets in Base 8

(55, 55+113, 98)-Net over F₈ — Constructive and digital

Digital (55, 168, 98)-net over F₈, using

t-expansion [i] based on digital (37, 168, 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]

(55, 55+113, 144)-Net over F₈ — Digital

Digital (55, 168, 144)-net over F₈, using

t-expansion [i] based on digital (45, 168, 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]

(55, 55+113, 1494)-Net in Base 8 — Upper bound on s

There is no (55, 168, 1495)-net in base 8, because

1 times m-reduction [i] would yield (55, 167, 1495)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 612401 559108 984807 062880 633569 957983 897971 241820 689873 958346 516308 665934 783205 209816 856975 818848 320437 880104 946906 927271 007274 040752 509317 436904 671144 > 8¹⁶⁷ [i]