MinT - Best Known (168−104, 168, s)-Nets in Base 4

Best Known (168−104, 168, s)-Nets in Base 4

(168−104, 168, 66)-Net over F₄ — Constructive and digital

Digital (64, 168, 66)-net over F₄, using

t-expansion [i] based on digital (49, 168, 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]

(168−104, 168, 99)-Net over F₄ — Digital

Digital (64, 168, 99)-net over F₄, using

t-expansion [i] based on digital (61, 168, 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]

(168−104, 168, 552)-Net in Base 4 — Upper bound on s

There is no (64, 168, 553)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 146895 612751 818074 910116 262327 645932 921241 539554 773233 477194 749360 092121 611395 159230 263157 063245 969344 > 4¹⁶⁸ [i]