Best Known (14, 25, s)-Nets in Base 25
(14, 25, 182)-Net over F25 — Constructive and digital
Digital (14, 25, 182)-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, 1, 26)-net over F25 (see above)
- 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
(14, 25, 690)-Net over F25 — Digital
Digital (14, 25, 690)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2525, 690, F25, 11) (dual of [690, 665, 12]-code), using
- 58 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 9 times 0, 1, 45 times 0) [i] based on linear OA(2521, 628, F25, 11) (dual of [628, 607, 12]-code), using
- construction XX applied to C1 = C([623,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([623,9]) [i] based on
- 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(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [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(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([623,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([623,9]) [i] based on
- 58 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 9 times 0, 1, 45 times 0) [i] based on linear OA(2521, 628, F25, 11) (dual of [628, 607, 12]-code), using
(14, 25, 556846)-Net in Base 25 — Upper bound on s
There is no (14, 25, 556847)-net in base 25, because
- 1 times m-reduction [i] would yield (14, 24, 556847)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 3552 736479 343010 056045 485880 893961 > 2524 [i]