Best Known (79, 99, s)-Nets in Base 5
(79, 99, 1564)-Net over F5 — Constructive and digital
Digital (79, 99, 1564)-net over F5, using
- net defined by OOA [i] based on linear OOA(599, 1564, F5, 20, 20) (dual of [(1564, 20), 31181, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(599, 15640, F5, 20) (dual of [15640, 15541, 21]-code), using
- construction XX applied to Ce(20) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(51, 14, F5, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(20) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- OA 10-folding and stacking [i] based on linear OA(599, 15640, F5, 20) (dual of [15640, 15541, 21]-code), using
(79, 99, 12054)-Net over F5 — Digital
Digital (79, 99, 12054)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(599, 12054, F5, 20) (dual of [12054, 11955, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(599, 15632, F5, 20) (dual of [15632, 15533, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(597, 15626, F5, 21) (dual of [15626, 15529, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(585, 15626, F5, 17) (dual of [15626, 15541, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(599, 15632, F5, 20) (dual of [15632, 15533, 21]-code), using
(79, 99, large)-Net in Base 5 — Upper bound on s
There is no (79, 99, large)-net in base 5, because
- 18 times m-reduction [i] would yield (79, 81, large)-net in base 5, but