MinT - Best Known (252−170, 252, s)-Nets in Base 4

Best Known (252−170, 252, s)-Nets in Base 4

(252−170, 252, 104)-Net over F₄ — Constructive and digital

Digital (82, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(252−170, 252, 129)-Net over F₄ — Digital

Digital (82, 252, 129)-net over F₄, using

t-expansion [i] based on digital (81, 252, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(252−170, 252, 591)-Net in Base 4 — Upper bound on s

There is no (82, 252, 592)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55 681745 927725 833863 765388 503581 596523 054230 414874 641719 684051 446257 728300 347738 608093 576948 134592 698389 596207 707820 182263 748975 897402 458124 722927 263520 > 4²⁵² [i]