MinT - Best Known (171−121, 171, s)-Nets in Base 8

Best Known (171−121, 171, s)-Nets in Base 8

(171−121, 171, 98)-Net over F₈ — Constructive and digital

Digital (50, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−121, 171, 144)-Net over F₈ — Digital

Digital (50, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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]

(171−121, 171, 1161)-Net in Base 8 — Upper bound on s

There is no (50, 171, 1162)-net in base 8, because

1 times m-reduction [i] would yield (50, 170, 1162)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3390 730012 360696 988203 123869 339602 208693 530668 849249 386897 879904 380888 476593 803130 205193 488531 681063 173054 361351 404228 008652 189603 100303 715908 563572 062432 > 8¹⁷⁰ [i]