MinT - Best Known (45, 146, s)-Nets in Base 8

Best Known (45, 146, s)-Nets in Base 8

(45, 146, 98)-Net over F₈ — Constructive and digital

Digital (45, 146, 98)-net over F₈, using

t-expansion [i] based on digital (37, 146, 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]

(45, 146, 144)-Net over F₈ — Digital

Digital (45, 146, 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]

(45, 146, 1126)-Net in Base 8 — Upper bound on s

There is no (45, 146, 1127)-net in base 8, because

1 times m-reduction [i] would yield (45, 145, 1127)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 92138 610651 909099 396165 951890 595203 459789 285299 654993 486110 461969 290045 356289 975020 753845 992292 944440 905122 824140 456618 346271 253524 > 8¹⁴⁵ [i]