MinT - Best Known (51, 51+116, s)-Nets in Base 8

Best Known (51, 51+116, s)-Nets in Base 8

(51, 51+116, 98)-Net over F₈ — Constructive and digital

Digital (51, 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]

(51, 51+116, 144)-Net over F₈ — Digital

Digital (51, 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]

(51, 51+116, 1241)-Net in Base 8 — Upper bound on s

There is no (51, 167, 1242)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 800550 294083 336951 570621 972591 397201 625280 283958 467602 839296 035091 699932 307198 033973 074460 859021 846111 229732 799573 661189 217056 103085 496966 433600 580864 > 8¹⁶⁷ [i]