Best Known (35, 51, s)-Nets in Base 25
(35, 51, 1956)-Net over F25 — Constructive and digital
Digital (35, 51, 1956)-net over F25, using
- net defined by OOA [i] based on linear OOA(2551, 1956, F25, 16, 16) (dual of [(1956, 16), 31245, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2551, 15648, F25, 16) (dual of [15648, 15597, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- OA 8-folding and stacking [i] based on linear OA(2551, 15648, F25, 16) (dual of [15648, 15597, 17]-code), using
(35, 51, 15648)-Net over F25 — Digital
Digital (35, 51, 15648)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2551, 15648, F25, 16) (dual of [15648, 15597, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
(35, 51, large)-Net in Base 25 — Upper bound on s
There is no (35, 51, large)-net in base 25, because
- 14 times m-reduction [i] would yield (35, 37, large)-net in base 25, but