Best Known (35, 35+13, s)-Nets in Base 25
(35, 35+13, 2813)-Net over F25 — Constructive and digital
Digital (35, 48, 2813)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (5, 11, 209)-net over F25, using
- net defined by OOA [i] based on linear OOA(2511, 209, F25, 6, 6) (dual of [(209, 6), 1243, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2511, 627, F25, 6) (dual of [627, 616, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(2511, 625, F25, 6) (dual of [625, 614, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(259, 625, F25, 5) (dual of [625, 616, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(2511, 627, F25, 6) (dual of [627, 616, 7]-code), using
- net defined by OOA [i] based on linear OOA(2511, 209, F25, 6, 6) (dual of [(209, 6), 1243, 7]-NRT-code), using
- digital (24, 37, 2604)-net over F25, using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- digital (5, 11, 209)-net over F25, using
(35, 35+13, 86088)-Net over F25 — Digital
Digital (35, 48, 86088)-net over F25, using
(35, 35+13, large)-Net in Base 25 — Upper bound on s
There is no (35, 48, large)-net in base 25, because
- 11 times m-reduction [i] would yield (35, 37, large)-net in base 25, but