MinT - Best Known (256−56, 256, s)-Nets in Base 4

Best Known (256−56, 256, s)-Nets in Base 4

(256−56, 256, 1539)-Net over F₄ — Constructive and digital

Digital (200, 256, 1539)-net over F₄, using

2 times m-reduction [i] based on digital (200, 258, 1539)-net over F₄, using
- trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(256−56, 256, 4539)-Net over F₄ — Digital

Digital (200, 256, 4539)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−56, 256, 1203438)-Net in Base 4 — Upper bound on s

There is no (200, 256, 1203439)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13407 855245 727781 238552 391776 864572 010386 907583 315782 343219 478046 093810 000125 364695 959078 752109 851495 018474 688805 727753 426287 463326 861288 982162 237548 931650 > 4²⁵⁶ [i]