MinT - Best Known (172−112, 172, s)-Nets in Base 8

Best Known (172−112, 172, s)-Nets in Base 8

(172−112, 172, 98)-Net over F₈ — Constructive and digital

Digital (60, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 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]

(172−112, 172, 144)-Net over F₈ — Digital

Digital (60, 172, 144)-net over F₈, using

t-expansion [i] based on digital (45, 172, 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]

(172−112, 172, 1806)-Net in Base 8 — Upper bound on s

There is no (60, 172, 1807)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 215638 376223 609955 873043 094581 362967 246848 665206 274408 011644 186109 469809 293131 187021 073260 159828 093300 905946 440688 045705 063137 371346 624553 191393 299314 144240 > 8¹⁷² [i]