MinT - Best Known (20, 20+40, s)-Nets in Base 256

Best Known (20, 20+40, s)-Nets in Base 256

(20, 20+40, 514)-Net over F₂₅₆ — Constructive and digital

Digital (20, 60, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 20, 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]
2. digital (0, 40, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(20, 20+40, 546359)-Net in Base 256 — Upper bound on s

There is no (20, 60, 546360)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 121829 588369 495894 677644 620164 485027 845653 859844 781537 069237 055923 475676 987481 517064 545095 596492 755318 233904 490409 051622 703080 602004 676392 653501 > 256⁶⁰ [i]