MinT - Best Known (57, 57+110, s)-Nets in Base 8

Best Known (57, 57+110, s)-Nets in Base 8

(57, 57+110, 98)-Net over F₈ — Constructive and digital

Digital (57, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(57, 57+110, 144)-Net over F₈ — Digital

Digital (57, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(57, 57+110, 1648)-Net in Base 8 — Upper bound on s

There is no (57, 167, 1649)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 613363 542759 579754 364955 294509 530910 130485 117046 834924 787729 418461 486588 830832 351568 369337 105848 573348 633011 871844 028288 013968 409963 140831 584285 975744 > 8¹⁶⁷ [i]