MinT - Best Known (60, 151, s)-Nets in Base 8

Best Known (60, 151, s)-Nets in Base 8

(60, 151, 98)-Net over F₈ — Constructive and digital

Digital (60, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(60, 151, 144)-Net over F₈ — Digital

Digital (60, 151, 144)-net over F₈, using

t-expansion [i] based on digital (45, 151, 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]

(60, 151, 2550)-Net in Base 8 — Upper bound on s

There is no (60, 151, 2551)-net in base 8, because

1 times m-reduction [i] would yield (60, 150, 2551)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2947 396428 266803 451578 917700 682249 687272 340883 901295 387977 646435 866590 262603 827250 987376 423760 653244 208665 074359 561658 312017 057130 197332 > 8¹⁵⁰ [i]