MinT - Best Known (14, 34, s)-Nets in Base 256

Best Known (14, 34, s)-Nets in Base 256

(14, 34, 518)-Net over F₂₅₆ — Constructive and digital

Digital (14, 34, 518)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 12, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]
2. digital (2, 22, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(14, 34, 763)-Net over F₂₅₆ — Digital

Digital (14, 34, 763)-net over F₂₅₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256³⁴, 763, F₂₅₆, 20) (dual of [763, 729, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(256³⁴, 771, F₂₅₆, 20) (dual of [771, 737, 21]-code), using
  - the BCH-code C(I) with length 771Â | 256²âˆ’1, defining interval IÂ =Â {117,118,…,136}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

(14, 34, 2738112)-Net in Base 256 — Upper bound on s

There is no (14, 34, 2738113)-net in base 256, because

the generalized Rao bound for nets shows that 256^mÂ â‰¥ 7588 564732 059635 387190 695151 565117 336038 472369 065552 124007 504630 943943 041858 671776 > 256³⁴ [i]