MinT - Best Known (23, 23+14, s)-Nets in Base 256

Best Known (23, 23+14, s)-Nets in Base 256

(23, 23+14, 9876)-Net over F₂₅₆ — Constructive and digital

Digital (23, 37, 9876)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 10, 514)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256¹⁰, 514, F₂₅₆, 7, 7) (dual of [(514, 7), 3588, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(256¹⁰, 514, F₂₅₆, 6, 7) (dual of [(514, 6), 3074, 8]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(256³, 257, F₂₅₆, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1539,256) [i]
        linear OOA(256⁷, 257, F₂₅₆, 6, 7) (dual of [(257, 6), 1535, 8]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1535,256) [i]
2. digital (13, 27, 9362)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256²⁷, 9362, F₂₅₆, 14, 14) (dual of [(9362, 14), 131041, 15]-NRT-code), using
    - OA 7-folding and stacking [i] based on linear OA(256²⁷, 65534, F₂₅₆, 14) (dual of [65534, 65507, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(256²⁷, 65536, F₂₅₆, 14) (dual of [65536, 65509, 15]-code), using
        an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

(23, 23+14, 158893)-Net over F₂₅₆ — Digital

Digital (23, 37, 158893)-net over F₂₅₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(23, 23+14, large)-Net in Base 256 — Upper bound on s

There is no (23, 37, large)-net in base 256, because

12 times m-reduction [i] would yield (23, 25, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]