MinT - Best Known (64, 64+103, s)-Nets in Base 8

Best Known (64, 64+103, s)-Nets in Base 8

(64, 64+103, 98)-Net over F₈ — Constructive and digital

Digital (64, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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+103, 144)-Net over F₈ — Digital

Digital (64, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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+103, 2435)-Net in Base 8 — Upper bound on s

There is no (64, 167, 2436)-net in base 8, because

1 times m-reduction [i] would yield (64, 166, 2436)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 832487 187418 493821 864134 909600 625181 961756 595145 039075 749221 226265 069623 449394 980715 762723 445519 295787 686019 223336 575650 115132 046108 339671 800882 383656 > 8¹⁶⁶ [i]