MinT - Best Known (59, 59+92, s)-Nets in Base 8

Best Known (59, 59+92, s)-Nets in Base 8

(59, 59+92, 98)-Net over F₈ — Constructive and digital

Digital (59, 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]

(59, 59+92, 144)-Net over F₈ — Digital

Digital (59, 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]

(59, 59+92, 2340)-Net in Base 8 — Upper bound on s

There is no (59, 151, 2341)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23553 553284 402605 887843 497423 035123 684809 304671 797965 907892 113693 292907 373303 496233 889275 074429 544432 190123 691869 686821 377315 323224 863616 > 8¹⁵¹ [i]