MinT - Best Known (133−87, 133, s)-Nets in Base 8

Best Known (133−87, 133, s)-Nets in Base 8

(133−87, 133, 98)-Net over F₈ — Constructive and digital

Digital (46, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(133−87, 133, 144)-Net over F₈ — Digital

Digital (46, 133, 144)-net over F₈, using

t-expansion [i] based on digital (45, 133, 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]

(133−87, 133, 1400)-Net in Base 8 — Upper bound on s

There is no (46, 133, 1401)-net in base 8, because

1 times m-reduction [i] would yield (46, 132, 1401)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 162633 947622 334512 406569 209412 427851 882600 932096 954612 307485 946220 399987 013067 905470 699742 292987 218745 111485 718469 648240 > 8¹³² [i]