MinT - Best Known (156−93, 156, s)-Nets in Base 8

Best Known (156−93, 156, s)-Nets in Base 8

(156−93, 156, 98)-Net over F₈ — Constructive and digital

Digital (63, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(156−93, 156, 144)-Net over F₈ — Digital

Digital (63, 156, 144)-net over F₈, using

t-expansion [i] based on digital (45, 156, 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]

(156−93, 156, 2809)-Net in Base 8 — Upper bound on s

There is no (63, 156, 2810)-net in base 8, because

1 times m-reduction [i] would yield (63, 155, 2810)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 370996 376272 130150 673862 840167 387871 147517 847074 931151 643242 533434 405968 157155 908404 952685 370075 190345 148145 948486 368046 838263 665124 744824 > 8¹⁵⁵ [i]