MinT - Best Known (66, 66+108, s)-Nets in Base 4

Best Known (66, 66+108, s)-Nets in Base 4

(66, 66+108, 66)-Net over F₄ — Constructive and digital

Digital (66, 174, 66)-net over F₄, using

t-expansion [i] based on digital (49, 174, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(66, 66+108, 99)-Net over F₄ — Digital

Digital (66, 174, 99)-net over F₄, using

t-expansion [i] based on digital (61, 174, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(66, 66+108, 565)-Net in Base 4 — Upper bound on s

There is no (66, 174, 566)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 605 666347 024992 839700 602601 837854 184184 635337 662292 488124 506557 754285 501855 939424 046157 654415 380718 570168 > 4¹⁷⁴ [i]