MinT - Best Known (168−96, 168, s)-Nets in Base 4

Best Known (168−96, 168, s)-Nets in Base 4

(168−96, 168, 66)-Net over F₄ — Constructive and digital

Digital (72, 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]

(168−96, 168, 105)-Net over F₄ — Digital

Digital (72, 168, 105)-net over F₄, using

t-expansion [i] based on digital (70, 168, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(168−96, 168, 760)-Net in Base 4 — Upper bound on s

There is no (72, 168, 761)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 141350 299105 560185 381262 912735 501843 554314 683306 781536 493714 765535 388339 392639 210699 958441 889583 358421 > 4¹⁶⁸ [i]