MinT - Best Known (9−5, 9, s)-Nets in Base 256

Best Known (9−5, 9, s)-Nets in Base 256

(9−5, 9, 32897)-Net over F₂₅₆ — Constructive and digital

Digital (4, 9, 32897)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256⁹, 32897, F₂₅₆, 5, 5) (dual of [(32897, 5), 164476, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(256⁹, 32897, F₂₅₆, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(256², 257, F₂₅₆, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;1026,256) [i]
    2. linear OOA(256⁷, 32640, F₂₅₆, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]

(9−5, 9, large)-Net in Base 256 — Upper bound on s

There is no (4, 9, large)-net in base 256, because

3 times m-reduction [i] would yield (4, 6, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]