MinT - Best Known (15−6, 15, s)-Nets in Base 25

Best Known (15−6, 15, s)-Nets in Base 25

(15−6, 15, 651)-Net over F₂₅ — Constructive and digital

Digital (9, 15, 651)-net over F₂₅, using

net defined by OOA [i] based on linear OOA(25¹⁵, 651, F₂₅, 6, 6) (dual of [(651, 6), 3891, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25¹⁵, 1953, F₂₅, 6) (dual of [1953, 1938, 7]-code), using
  - the BCH-code C(I) with length 1953Â | 25³âˆ’1, defining interval IÂ =Â {1,9,17,…,41}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

(15−6, 15, 1953)-Net over F₂₅ — Digital

Digital (9, 15, 1953)-net over F₂₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(25¹⁵, 1953, F₂₅, 6) (dual of [1953, 1938, 7]-code), using
- the BCH-code C(I) with length 1953Â | 25³âˆ’1, defining interval IÂ =Â {1,9,17,…,41}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

(15−6, 15, 739387)-Net in Base 25 — Upper bound on s

There is no (9, 15, 739388)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 931 325835 466511 563105 > 25¹⁵ [i]