MinT - Best Known (179−120, 179, s)-Nets in Base 4

Best Known (179−120, 179, s)-Nets in Base 4

(179−120, 179, 66)-Net over F₄ — Constructive and digital

Digital (59, 179, 66)-net over F₄, using

t-expansion [i] based on digital (49, 179, 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]

(179−120, 179, 91)-Net over F₄ — Digital

Digital (59, 179, 91)-net over F₄, using

t-expansion [i] based on digital (50, 179, 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]

(179−120, 179, 435)-Net in Base 4 — Upper bound on s

There is no (59, 179, 436)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 602048 022167 514299 643040 429604 515146 406232 744278 882098 797338 147605 604323 765089 325179 330751 505105 020489 252064 > 4¹⁷⁹ [i]