MinT - Best Known (165−106, 165, s)-Nets in Base 4

Best Known (165−106, 165, s)-Nets in Base 4

(165−106, 165, 66)-Net over F₄ — Constructive and digital

Digital (59, 165, 66)-net over F₄, using

t-expansion [i] based on digital (49, 165, 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]

(165−106, 165, 91)-Net over F₄ — Digital

Digital (59, 165, 91)-net over F₄, using

t-expansion [i] based on digital (50, 165, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(165−106, 165, 471)-Net in Base 4 — Upper bound on s

There is no (59, 165, 472)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2245 868450 229599 803602 482502 287077 037913 371888 535870 954386 874478 414288 369844 665403 762202 041489 124010 > 4¹⁶⁵ [i]