MinT - Best Known (100, 100+30, s)-Nets in Base 16

Best Known (100, 100+30, s)-Nets in Base 16

(100, 100+30, 8740)-Net over F₁₆ — Constructive and digital

Digital (100, 130, 8740)-net over F₁₆, using

16⁴ times duplication [i] based on digital (96, 126, 8740)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16¹²⁶, 8740, F₁₆, 30, 30) (dual of [(8740, 30), 262074, 31]-NRT-code), using
  - OA 15-folding and stacking [i] based on linear OA(16¹²⁶, 131100, F₁₆, 30) (dual of [131100, 130974, 31]-code), using
    - trace code [i] based on linear OA(256⁶³, 65550, F₂₅₆, 30) (dual of [65550, 65487, 31]-code), using
      - constructionÂ X applied to C_e(29) âŠ‚ C_e(24) [i] based on
        linear OA(256⁵⁹, 65536, F₂₅₆, 30) (dual of [65536, 65477, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
        linear OA(256⁴⁹, 65536, F₂₅₆, 25) (dual of [65536, 65487, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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]

(100, 100+30, 194465)-Net over F₁₆ — Digital

Digital (100, 130, 194465)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+30, large)-Net in Base 16 — Upper bound on s

There is no (100, 130, large)-net in base 16, because

28 times m-reduction [i] would yield (100, 102, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]