MinT - Best Known (24, 24+31, s)-Nets in Base 256

Best Known (24, 24+31, s)-Nets in Base 256

(24, 24+31, 523)-Net over F₂₅₆ — Constructive and digital

Digital (24, 55, 523)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (5, 36, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(24, 24+31, 1285)-Net over F₂₅₆ — Digital

Digital (24, 55, 1285)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256⁵⁵, 1285, F₂₅₆, 31) (dual of [1285, 1230, 32]-code), using
- the BCH-code C(I) with length 1285Â | 256²âˆ’1, defining interval IÂ =Â {1,138,275,…,256}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]

(24, 24+31, large)-Net in Base 256 — Upper bound on s

There is no (24, 55, large)-net in base 256, because

29 times m-reduction [i] would yield (24, 26, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]