Best Known (13, 23, s)-Nets in Base 25
(13, 23, 156)-Net over F25 — Constructive and digital
Digital (13, 23, 156)-net over F25, using
- 1 times m-reduction [i] based on digital (13, 24, 156)-net over F25, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 26)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 with arbitrarily large s, using
- digital (0, 2, 26)-net over F25, using
- digital (0, 2, 26)-net over F25 (see above)
- digital (0, 3, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (0, 5, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25 (see above)
- digital (0, 11, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25 (see above)
- digital (0, 1, 26)-net over F25, using
- generalized (u, u+v)-construction [i] based on
(13, 23, 728)-Net over F25 — Digital
Digital (13, 23, 728)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2523, 728, F25, 10) (dual of [728, 705, 11]-code), using
- 96 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 17 times 0, 1, 74 times 0) [i] based on linear OA(2519, 628, F25, 10) (dual of [628, 609, 11]-code), using
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- 96 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 17 times 0, 1, 74 times 0) [i] based on linear OA(2519, 628, F25, 10) (dual of [628, 609, 11]-code), using
(13, 23, 292513)-Net in Base 25 — Upper bound on s
There is no (13, 23, 292514)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 142 109999 938864 899748 969448 441713 > 2523 [i]