Best Known (14, 22, s)-Nets in Base 5
(14, 22, 104)-Net over F5 — Constructive and digital
Digital (14, 22, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 11, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
(14, 22, 149)-Net over F5 — Digital
Digital (14, 22, 149)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(522, 149, F5, 8) (dual of [149, 127, 9]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0) [i] based on linear OA(519, 130, F5, 8) (dual of [130, 111, 9]-code), using
- construction XX applied to C1 = C([123,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([123,6]) [i] based on
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(519, 124, F5, 8) (dual of [124, 105, 9]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([123,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([123,6]) [i] based on
- 16 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0) [i] based on linear OA(519, 130, F5, 8) (dual of [130, 111, 9]-code), using
(14, 22, 3864)-Net in Base 5 — Upper bound on s
There is no (14, 22, 3865)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2386 435620 537201 > 522 [i]