MinT - Best Known (52, 52+82, s)-Nets in Base 8

Best Known (52, 52+82, s)-Nets in Base 8

(52, 52+82, 98)-Net over F₈ — Constructive and digital

Digital (52, 134, 98)-net over F₈, using

t-expansion [i] based on digital (37, 134, 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]

(52, 52+82, 144)-Net over F₈ — Digital

Digital (52, 134, 144)-net over F₈, using

t-expansion [i] based on digital (45, 134, 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]

(52, 52+82, 2036)-Net in Base 8 — Upper bound on s

There is no (52, 134, 2037)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 398658 775740 473218 510637 510476 218977 230247 057303 607712 413919 013888 414345 496663 216055 051581 214643 936352 391405 976017 664600 > 8¹³⁴ [i]