MinT - Best Known (203−50, 203, s)-Nets in Base 4

Best Known (203−50, 203, s)-Nets in Base 4

(203−50, 203, 1028)-Net over F₄ — Constructive and digital

Digital (153, 203, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (153, 204, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 51, 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]

(203−50, 203, 2012)-Net over F₄ — Digital

Digital (153, 203, 2012)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−50, 203, 262541)-Net in Base 4 — Upper bound on s

There is no (153, 203, 262542)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 270843 714877 315476 060482 264418 884402 762037 132471 407504 374463 859441 933804 048825 599508 257733 049489 486528 852476 812098 164952 > 4²⁰³ [i]