MinT - Best Known (72, 94, s)-Nets in Base 16

Best Known (72, 94, s)-Nets in Base 16

(72, 94, 11918)-Net over F₁₆ — Constructive and digital

Digital (72, 94, 11918)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16⁹⁴, 11918, F₁₆, 22, 22) (dual of [(11918, 22), 262102, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(16⁹⁴, 131098, F₁₆, 22) (dual of [131098, 131004, 23]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹⁴, 131100, F₁₆, 22) (dual of [131100, 131006, 23]-code), using
    - trace code [i] based on linear OA(256⁴⁷, 65550, F₂₅₆, 22) (dual of [65550, 65503, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
        linear OA(256⁴³, 65536, F₂₅₆, 22) (dual of [65536, 65493, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(256³³, 65536, F₂₅₆, 17) (dual of [65536, 65503, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(256⁴, 14, F₂₅₆, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁴, 256, F₂₅₆, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
        Reedâ€“Solomon code RS(252,256) [i]

(72, 94, 142005)-Net over F₁₆ — Digital

Digital (72, 94, 142005)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 94, large)-Net in Base 16 — Upper bound on s

There is no (72, 94, large)-net in base 16, because

20 times m-reduction [i] would yield (72, 74, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]