MinT - Best Known (51, 173, s)-Nets in Base 8

Best Known (51, 173, s)-Nets in Base 8

(51, 173, 98)-Net over F₈ — Constructive and digital

Digital (51, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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, 173, 144)-Net over F₈ — Digital

Digital (51, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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, 173, 1187)-Net in Base 8 — Upper bound on s

There is no (51, 173, 1188)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 782124 051629 767429 120328 627942 805285 408879 244655 552908 640092 126474 335232 053665 245487 706239 654244 533249 296692 662702 242787 519847 837024 043279 667820 553907 039008 > 8¹⁷³ [i]