MinT - Best Known (194, 194+64, s)-Nets in Base 4

Best Known (194, 194+64, s)-Nets in Base 4

(194, 194+64, 1028)-Net over F₄ — Constructive and digital

Digital (194, 258, 1028)-net over F₄, using

4² times duplication [i] based on digital (192, 256, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 64, 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]

(194, 194+64, 2398)-Net over F₄ — Digital

Digital (194, 258, 2398)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194, 194+64, 304670)-Net in Base 4 — Upper bound on s

There is no (194, 258, 304671)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214534 760712 343653 880191 690172 464714 077463 979756 881450 007972 563698 780443 207533 742186 088380 919861 002240 798094 424674 245797 469258 618199 068507 416553 102198 826032 > 4²⁵⁸ [i]