Best Known (65, 65+30, s)-Nets in Base 25
(65, 65+30, 1043)-Net over F25 — Constructive and digital
Digital (65, 95, 1043)-net over F25, using
- 251 times duplication [i] based on digital (64, 94, 1043)-net over F25, using
- t-expansion [i] based on digital (63, 94, 1043)-net over F25, using
- net defined by OOA [i] based on linear OOA(2594, 1043, F25, 31, 31) (dual of [(1043, 31), 32239, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2594, 15646, F25, 31) (dual of [15646, 15552, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2594, 15649, F25, 31) (dual of [15649, 15555, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(23) [i] based on
- linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(256, 24, F25, 6) (dual of [24, 18, 7]-code or 24-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- construction X applied to Ce(30) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(2594, 15649, F25, 31) (dual of [15649, 15555, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2594, 15646, F25, 31) (dual of [15646, 15552, 32]-code), using
- net defined by OOA [i] based on linear OOA(2594, 1043, F25, 31, 31) (dual of [(1043, 31), 32239, 32]-NRT-code), using
- t-expansion [i] based on digital (63, 94, 1043)-net over F25, using
(65, 65+30, 18480)-Net over F25 — Digital
Digital (65, 95, 18480)-net over F25, using
(65, 65+30, large)-Net in Base 25 — Upper bound on s
There is no (65, 95, large)-net in base 25, because
- 28 times m-reduction [i] would yield (65, 67, large)-net in base 25, but