Best Known (7, 14, s)-Nets in Base 25
(7, 14, 210)-Net over F25 — Constructive and digital
Digital (7, 14, 210)-net over F25, using
- net defined by OOA [i] based on linear OOA(2514, 210, F25, 7, 7) (dual of [(210, 7), 1456, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2514, 631, F25, 7) (dual of [631, 617, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(2513, 626, F25, 7) (dual of [626, 613, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(259, 626, F25, 5) (dual of [626, 617, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(2514, 631, F25, 7) (dual of [631, 617, 8]-code), using
(7, 14, 466)-Net over F25 — Digital
Digital (7, 14, 466)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2514, 466, F25, 7) (dual of [466, 452, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2514, 624, F25, 7) (dual of [624, 610, 8]-code), using
(7, 14, 86478)-Net in Base 25 — Upper bound on s
There is no (7, 14, 86479)-net in base 25, because
- 1 times m-reduction [i] would yield (7, 13, 86479)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 490154 850303 931449 > 2513 [i]