MinT - Best Known (14, 14+19, s)-Nets in Base 256

Best Known (14, 14+19, s)-Nets in Base 256

(14, 14+19, 519)-Net over F₂₅₆ — Constructive and digital

Digital (14, 33, 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, 22, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(14, 14+19, 822)-Net over F₂₅₆ — Digital

Digital (14, 33, 822)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256³³, 822, F₂₅₆, 19) (dual of [822, 789, 20]-code), using
- 49 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 48 times 0) [i] based on linear OA(256³¹, 771, F₂₅₆, 19) (dual of [771, 740, 20]-code), using
  - the BCH-code C(I) with length 771Â | 256²âˆ’1, defining interval IÂ =Â {256,456,656,…,1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

(14, 14+19, 5940759)-Net in Base 256 — Upper bound on s

There is no (14, 33, 5940760)-net in base 256, because

1 times m-reduction [i] would yield (14, 32, 5940760)-net in base 256, but
- 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]