MinT - Best Known (51, 137, s)-Nets in Base 8

Best Known (51, 137, s)-Nets in Base 8

(51, 137, 98)-Net over F₈ — Constructive and digital

Digital (51, 137, 98)-net over F₈, using

t-expansion [i] based on digital (37, 137, 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]

(51, 137, 144)-Net over F₈ — Digital

Digital (51, 137, 144)-net over F₈, using

t-expansion [i] based on digital (45, 137, 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]

(51, 137, 1791)-Net in Base 8 — Upper bound on s

There is no (51, 137, 1792)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5383 726803 883346 492707 043135 047199 889972 728607 779751 250509 273858 071946 394449 100611 547334 203336 024635 802669 615907 691304 917945 > 8¹³⁷ [i]