MinT - Best Known (32−18, 32, s)-Nets in Base 256

Best Known (32−18, 32, s)-Nets in Base 256

(32−18, 32, 519)-Net over F₂₅₆ — Constructive and digital

Digital (14, 32, 519)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 11, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (3, 21, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(32−18, 32, 1229)-Net over F₂₅₆ — Digital

Digital (14, 32, 1229)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256³², 1229, F₂₅₆, 18) (dual of [1229, 1197, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(256³², 1285, F₂₅₆, 18) (dual of [1285, 1253, 19]-code), using
  - the BCH-code C(I) with length 1285Â | 256²âˆ’1, defining interval IÂ =Â {1,18,35,…,290}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

(32−18, 32, 5940759)-Net in Base 256 — Upper bound on s

There is no (14, 32, 5940760)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 115792 202694 689779 331905 441038 148523 183650 998899 198099 271630 262607 118796 956826 > 256³² [i]