Best Known (95, 95+20, s)-Nets in Base 5
(95, 95+20, 7814)-Net over F5 — Constructive and digital
Digital (95, 115, 7814)-net over F5, using
- 1 times m-reduction [i] based on digital (95, 116, 7814)-net over F5, using
- net defined by OOA [i] based on linear OOA(5116, 7814, F5, 21, 21) (dual of [(7814, 21), 163978, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5116, 78141, F5, 21) (dual of [78141, 78025, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5116, 78141, F5, 21) (dual of [78141, 78025, 22]-code), using
- net defined by OOA [i] based on linear OOA(5116, 7814, F5, 21, 21) (dual of [(7814, 21), 163978, 22]-NRT-code), using
(95, 95+20, 50440)-Net over F5 — Digital
Digital (95, 115, 50440)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5115, 50440, F5, 20) (dual of [50440, 50325, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 78132, F5, 20) (dual of [78132, 78017, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(599, 78126, F5, 17) (dual of [78126, 78027, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, 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(5115, 78132, F5, 20) (dual of [78132, 78017, 21]-code), using
(95, 95+20, large)-Net in Base 5 — Upper bound on s
There is no (95, 115, large)-net in base 5, because
- 18 times m-reduction [i] would yield (95, 97, large)-net in base 5, but