Best Known (33−11, 33, s)-Nets in Base 25
(33−11, 33, 3127)-Net over F25 — Constructive and digital
Digital (22, 33, 3127)-net over F25, using
- net defined by OOA [i] based on linear OOA(2533, 3127, F25, 11, 11) (dual of [(3127, 11), 34364, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2533, 15636, F25, 11) (dual of [15636, 15603, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(2531, 15625, F25, 11) (dual of [15625, 15594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2522, 15625, F25, 8) (dual of [15625, 15603, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(2533, 15636, F25, 11) (dual of [15636, 15603, 12]-code), using
(33−11, 33, 15636)-Net over F25 — Digital
Digital (22, 33, 15636)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2533, 15636, F25, 11) (dual of [15636, 15603, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(2531, 15625, F25, 11) (dual of [15625, 15594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2522, 15625, F25, 8) (dual of [15625, 15603, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
(33−11, 33, large)-Net in Base 25 — Upper bound on s
There is no (22, 33, large)-net in base 25, because
- 9 times m-reduction [i] would yield (22, 24, large)-net in base 25, but