MinT - Best Known (164−118, 164, s)-Nets in Base 8

Best Known (164−118, 164, s)-Nets in Base 8

(164−118, 164, 98)-Net over F₈ — Constructive and digital

Digital (46, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(164−118, 164, 144)-Net over F₈ — Digital

Digital (46, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(164−118, 164, 1018)-Net in Base 8 — Upper bound on s

There is no (46, 164, 1019)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13053 430391 639887 206096 521287 687683 261608 551654 431724 073029 228256 849128 670036 656764 800412 084523 789458 022715 967066 875943 445783 904528 354429 411656 120808 > 8¹⁶⁴ [i]