MinT - Best Known (3, 9, s)-Nets in Base 256

Best Known (3, 9, s)-Nets in Base 256

(3, 9, 514)-Net over F₂₅₆ — Constructive and digital

Digital (3, 9, 514)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁹, 514, F₂₅₆, 6, 6) (dual of [(514, 6), 3075, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(256⁹, 514, F₂₅₆, 5, 6) (dual of [(514, 5), 2561, 7]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256³, 257, F₂₅₆, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;1282,256) [i]
    2. linear OOA(256⁶, 257, F₂₅₆, 5, 6) (dual of [(257, 5), 1279, 7]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(5;1279,256) [i]

(3, 9, 119552)-Net in Base 256 — Upper bound on s

There is no (3, 9, 119553)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 4722 388935 250701 258496 > 256⁹ [i]