MinT - Best Known (53, 53+112, s)-Nets in Base 8

Best Known (53, 53+112, s)-Nets in Base 8

(53, 53+112, 98)-Net over F₈ — Constructive and digital

Digital (53, 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]

(53, 53+112, 144)-Net over F₈ — Digital

Digital (53, 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]

(53, 53+112, 1385)-Net in Base 8 — Upper bound on s

There is no (53, 165, 1386)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105413 066592 790530 372889 916571 174459 440548 198892 517173 229433 196804 309254 121141 431511 012691 933070 503716 866067 504702 125604 027141 320268 149028 704453 598644 > 8¹⁶⁵ [i]