MinT - Best Known (249−62, 249, s)-Nets in Base 4

Best Known (249−62, 249, s)-Nets in Base 4

(249−62, 249, 1028)-Net over F₄ — Constructive and digital

Digital (187, 249, 1028)-net over F₄, using

4¹ times duplication [i] based on digital (186, 248, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 62, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(249−62, 249, 2283)-Net over F₄ — Digital

Digital (187, 249, 2283)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−62, 249, 283644)-Net in Base 4 — Upper bound on s

There is no (187, 249, 283645)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818405 568072 631986 652078 068634 162263 916437 829163 702312 438098 761682 013626 383230 642225 649395 412380 904660 110070 753290 682290 364777 508123 751977 109136 996832 > 4²⁴⁹ [i]