Best Known (17, 29, s)-Nets in Base 32
(17, 29, 204)-Net over F32 — Constructive and digital
Digital (17, 29, 204)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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 (11, 23, 171)-net over F32, using
- net defined by OOA [i] based on linear OOA(3223, 171, F32, 12, 12) (dual of [(171, 12), 2029, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- net defined by OOA [i] based on linear OOA(3223, 171, F32, 12, 12) (dual of [(171, 12), 2029, 13]-NRT-code), using
- digital (0, 6, 33)-net over F32, using
(17, 29, 683)-Net in Base 32 — Constructive
(17, 29, 683)-net in base 32, using
- 321 times duplication [i] based on (16, 28, 683)-net in base 32, using
- net defined by OOA [i] based on OOA(3228, 683, S32, 12, 12), using
- OA 6-folding and stacking [i] based on OA(3228, 4098, S32, 12), using
- discarding parts of the base [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(6423, 4098, F64, 12) (dual of [4098, 4075, 13]-code), using
- OA 6-folding and stacking [i] based on OA(3228, 4098, S32, 12), using
- net defined by OOA [i] based on OOA(3228, 683, S32, 12, 12), using
(17, 29, 1505)-Net over F32 — Digital
Digital (17, 29, 1505)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3229, 1505, F32, 12) (dual of [1505, 1476, 13]-code), using
- 472 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 31 times 0, 1, 125 times 0, 1, 307 times 0) [i] based on linear OA(3223, 1027, F32, 12) (dual of [1027, 1004, 13]-code), using
- construction XX applied to C1 = C([1022,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([1022,10]) [i] based on
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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([1022,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([1022,10]) [i] based on
- 472 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 31 times 0, 1, 125 times 0, 1, 307 times 0) [i] based on linear OA(3223, 1027, F32, 12) (dual of [1027, 1004, 13]-code), using
(17, 29, 1818659)-Net in Base 32 — Upper bound on s
There is no (17, 29, 1818660)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 44 601618 176940 753363 253438 133787 388313 970808 > 3229 [i]