MinT - Best Known (53, 53+77, s)-Nets in Base 8

Best Known (53, 53+77, s)-Nets in Base 8

(53, 53+77, 98)-Net over F₈ — Constructive and digital

Digital (53, 130, 98)-net over F₈, using

t-expansion [i] based on digital (37, 130, 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+77, 144)-Net over F₈ — Digital

Digital (53, 130, 144)-net over F₈, using

t-expansion [i] based on digital (45, 130, 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+77, 2473)-Net in Base 8 — Upper bound on s

There is no (53, 130, 2474)-net in base 8, because

1 times m-reduction [i] would yield (53, 129, 2474)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 318 262073 011256 661948 011486 474467 220174 334760 912949 364123 556811 187772 635624 641913 461019 766160 219342 125488 877595 681940 > 8¹²⁹ [i]