MinT - Best Known (164−98, 164, s)-Nets in Base 8

Best Known (164−98, 164, s)-Nets in Base 8

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

Digital (66, 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]

(164−98, 164, 144)-Net over F₈ — Digital

Digital (66, 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]

(164−98, 164, 2845)-Net in Base 8 — Upper bound on s

There is no (66, 164, 2846)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12971 941438 716061 225789 600972 306222 378374 949576 750896 724947 469094 131629 963617 815680 742086 238253 448810 952896 126892 702541 448453 432955 435013 224204 340664 > 8¹⁶⁴ [i]