MinT - Best Known (67, 67+100, s)-Nets in Base 8

Best Known (67, 67+100, s)-Nets in Base 8

(67, 67+100, 98)-Net over F₈ — Constructive and digital

Digital (67, 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]

(67, 67+100, 144)-Net over F₈ — Digital

Digital (67, 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]

(67, 67+100, 2858)-Net in Base 8 — Upper bound on s

There is no (67, 167, 2859)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 618541 060632 626133 744417 874873 253033 836627 154517 607656 101239 920001 731664 050509 397824 769045 131676 295957 216869 488725 440663 190070 285985 199095 979471 973136 > 8¹⁶⁷ [i]