Best Known (15, 25, s)-Nets in Base 32
(15, 25, 264)-Net over F32 — Constructive and digital
Digital (15, 25, 264)-net over F32, using
- 1 times m-reduction [i] based on digital (15, 26, 264)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 11, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(15, 25, 820)-Net in Base 32 — Constructive
(15, 25, 820)-net in base 32, using
- 321 times duplication [i] based on (14, 24, 820)-net in base 32, using
- base change [i] based on digital (10, 20, 820)-net over F64, using
- net defined by OOA [i] based on linear OOA(6420, 820, F64, 10, 10) (dual of [(820, 10), 8180, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6420, 4100, F64, 10) (dual of [4100, 4080, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6420, 4101, F64, 10) (dual of [4101, 4081, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(6420, 4101, F64, 10) (dual of [4101, 4081, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6420, 4100, F64, 10) (dual of [4100, 4080, 11]-code), using
- net defined by OOA [i] based on linear OOA(6420, 820, F64, 10, 10) (dual of [(820, 10), 8180, 11]-NRT-code), using
- base change [i] based on digital (10, 20, 820)-net over F64, using
(15, 25, 2039)-Net over F32 — Digital
Digital (15, 25, 2039)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3225, 2039, F32, 10) (dual of [2039, 2014, 11]-code), using
- 1006 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 15 times 0, 1, 81 times 0, 1, 294 times 0, 1, 610 times 0) [i] based on linear OA(3219, 1027, F32, 10) (dual of [1027, 1008, 11]-code), using
- construction XX applied to C1 = C([1022,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([1022,8]) [i] based on
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3215, 1023, F32, 8) (dual of [1023, 1008, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([1022,8]) [i] based on
- 1006 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 15 times 0, 1, 81 times 0, 1, 294 times 0, 1, 610 times 0) [i] based on linear OA(3219, 1027, F32, 10) (dual of [1027, 1008, 11]-code), using
(15, 25, 2050)-Net in Base 32
(15, 25, 2050)-net in base 32, using
- 321 times duplication [i] based on (14, 24, 2050)-net in base 32, using
- base change [i] based on digital (10, 20, 2050)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6420, 2050, F64, 2, 10) (dual of [(2050, 2), 4080, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6420, 4100, F64, 10) (dual of [4100, 4080, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6420, 4101, F64, 10) (dual of [4101, 4081, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(6420, 4101, F64, 10) (dual of [4101, 4081, 11]-code), using
- OOA 2-folding [i] based on linear OA(6420, 4100, F64, 10) (dual of [4100, 4080, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6420, 2050, F64, 2, 10) (dual of [(2050, 2), 4080, 11]-NRT-code), using
- base change [i] based on digital (10, 20, 2050)-net over F64, using
(15, 25, 2819837)-Net in Base 32 — Upper bound on s
There is no (15, 25, 2819838)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 42 535317 737694 264682 434906 410655 799829 > 3225 [i]