MinT - Best Known (131−81, 131, s)-Nets in Base 8

Best Known (131−81, 131, s)-Nets in Base 8

(131−81, 131, 98)-Net over F₈ — Constructive and digital

Digital (50, 131, 98)-net over F₈, using

t-expansion [i] based on digital (37, 131, 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]

(131−81, 131, 144)-Net over F₈ — Digital

Digital (50, 131, 144)-net over F₈, using

t-expansion [i] based on digital (45, 131, 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]

(131−81, 131, 1914)-Net in Base 8 — Upper bound on s

There is no (50, 131, 1915)-net in base 8, because

1 times m-reduction [i] would yield (50, 130, 1915)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2543 162630 740448 263016 185031 290416 733549 255910 902954 455951 253170 032550 025454 604654 957243 813463 152235 249809 448191 654435 > 8¹³⁰ [i]