MinT - Best Known (256−164, 256, s)-Nets in Base 4

Best Known (256−164, 256, s)-Nets in Base 4

(256−164, 256, 104)-Net over F₄ — Constructive and digital

Digital (92, 256, 104)-net over F₄, using

t-expansion [i] based on digital (73, 256, 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]

(256−164, 256, 144)-Net over F₄ — Digital

Digital (92, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(256−164, 256, 725)-Net in Base 4 — Upper bound on s

There is no (92, 256, 726)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13471 774229 907664 360601 181482 074089 550938 778404 416302 700540 667782 982002 787986 668220 044288 855099 480062 908642 659532 539549 361876 254899 113435 471420 327167 713814 > 4²⁵⁶ [i]