MinT - Best Known (64, 64+91, s)-Nets in Base 8

Best Known (64, 64+91, s)-Nets in Base 8

(64, 64+91, 98)-Net over F₈ — Constructive and digital

Digital (64, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(64, 64+91, 144)-Net over F₈ — Digital

Digital (64, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(64, 64+91, 3073)-Net in Base 8 — Upper bound on s

There is no (64, 155, 3074)-net in base 8, because

1 times m-reduction [i] would yield (64, 154, 3074)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 958674 400632 280935 060156 472673 323611 324016 673190 116647 456489 768714 333409 724673 088623 943353 260850 043157 649939 452409 123343 992067 073347 501312 > 8¹⁵⁴ [i]