MinT - Best Known (55, 165, s)-Nets in Base 8

Best Known (55, 165, s)-Nets in Base 8

(55, 165, 98)-Net over F₈ — Constructive and digital

Digital (55, 165, 98)-net over F₈, using

t-expansion [i] based on digital (37, 165, 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]

(55, 165, 144)-Net over F₈ — Digital

Digital (55, 165, 144)-net over F₈, using

t-expansion [i] based on digital (45, 165, 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]

(55, 165, 1526)-Net in Base 8 — Upper bound on s

There is no (55, 165, 1527)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105537 958885 396864 372400 950669 633166 393377 465445 290259 272741 181536 814035 153835 164811 224239 942465 738770 314332 899850 620117 223180 413062 824030 541980 215368 > 8¹⁶⁵ [i]