MinT - Best Known (64, 64+109, s)-Nets in Base 8

Best Known (64, 64+109, s)-Nets in Base 8

(64, 64+109, 98)-Net over F₈ — Constructive and digital

Digital (64, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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+109, 144)-Net over F₈ — Digital

Digital (64, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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+109, 2219)-Net in Base 8 — Upper bound on s

There is no (64, 173, 2220)-net in base 8, because

1 times m-reduction [i] would yield (64, 172, 2220)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214826 750277 329016 084080 495859 261902 770739 410810 670590 974970 501590 486696 725591 502967 519607 318183 486186 235358 475372 363816 759242 904636 888676 378146 462968 124912 > 8¹⁷² [i]