MinT - Best Known (19, 19+24, s)-Nets in Base 256

Best Known (19, 19+24, s)-Nets in Base 256

(19, 19+24, 521)-Net over F₂₅₆ — Constructive and digital

Digital (19, 43, 521)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 15, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (4, 28, 261)-net over F₂₅₆, using
  - net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(19, 19+24, 1285)-Net over F₂₅₆ — Digital

Digital (19, 43, 1285)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256⁴³, 1285, F₂₅₆, 24) (dual of [1285, 1242, 25]-code), using
- the BCH-code C(I) with length 1285Â | 256²âˆ’1, defining interval IÂ =Â {1,78,155,…,487}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]

(19, 19+24, large)-Net in Base 256 — Upper bound on s

There is no (19, 43, large)-net in base 256, because

22 times m-reduction [i] would yield (19, 21, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]