MinT - Best Known (14, 14+5, s)-Nets in Base 16

Best Known (14, 14+5, s)-Nets in Base 16

(14, 14+5, 130561)-Net over F₁₆ — Constructive and digital

Digital (14, 19, 130561)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹⁹, 130561, F₁₆, 6, 5) (dual of [(130561, 6), 783347, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(16¹⁹, 130562, F₁₆, 2, 5) (dual of [(130562, 2), 261105, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(16⁵, 69905, F₁₆, 2, 2) (dual of [(69905, 2), 139805, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
        Hamming code H(5,16) [i]
    2. linear OOA(16¹⁴, 65281, F₁₆, 2, 5) (dual of [(65281, 2), 130548, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
        trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]

(14, 14+5, 200467)-Net over F₁₆ — Digital

Digital (14, 19, 200467)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16¹⁹, 200467, F₁₆, 5) (dual of [200467, 200448, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(16⁵, 69905, F₁₆, 2) (dual of [69905, 69900, 3]-code), using
    - Hamming code H(5,16) [i]
  2. linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
    - trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [i]

(14, 14+5, large)-Net in Base 16 — Upper bound on s

There is no (14, 19, large)-net in base 16, because

3 times m-reduction [i] would yield (14, 16, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]