MinT - Best Known (21, 21+4, s)-Nets in Base 25

Best Known (21, 21+4, s)-Nets in Base 25

(21, 21+4, large)-Net over F₂₅ — Constructive and digital

Digital (21, 25, large)-net over F₂₅, using

25¹ times duplication [i] based on digital (20, 24, large)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (4, 6, large)-net over F₂₅, using
    - kÂ =Â 2 construction [i]
  2. digital (14, 18, 4194327)-net over F₂₅, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 2, 26)-net over F₂₅, using
        kÂ =Â 2 construction [i]
      2. digital (12, 16, 4194301)-net over F₂₅, using
        net defined by OOA [i] based on linear OOA(25¹⁶, 4194301, F₂₅, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(25¹⁶, 8388602, F₂₅, 4) (dual of [8388602, 8388586, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹⁶, large, F₂₅, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

(21, 21+4, large)-Net in Base 25 — Upper bound on s

There is no (21, 25, large)-net in base 25, because

2 times m-reduction [i] would yield (21, 23, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]