MinT - Best Known (257−64, 257, s)-Nets in Base 4

Best Known (257−64, 257, s)-Nets in Base 4

(257−64, 257, 1028)-Net over F₄ — Constructive and digital

Digital (193, 257, 1028)-net over F₄, using

4¹ 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]

(257−64, 257, 2346)-Net over F₄ — Digital

Digital (193, 257, 2346)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−64, 257, 291752)-Net in Base 4 — Upper bound on s

There is no (193, 257, 291753)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53634 632338 120185 884016 236354 106217 859452 660666 895180 326708 716541 693180 902888 758810 175341 653317 548276 553611 102456 246772 210410 704419 167022 194557 437870 243793 > 4²⁵⁷ [i]