Best Known (103−28, 103, s)-Nets in Base 32
(103−28, 103, 2438)-Net over F32 — Constructive and digital
Digital (75, 103, 2438)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 21, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (54, 82, 2340)-net over F32, using
- net defined by OOA [i] based on linear OOA(3282, 2340, F32, 28, 28) (dual of [(2340, 28), 65438, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3282, 32760, F32, 28) (dual of [32760, 32678, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3282, 32760, F32, 28) (dual of [32760, 32678, 29]-code), using
- net defined by OOA [i] based on linear OOA(3282, 2340, F32, 28, 28) (dual of [(2340, 28), 65438, 29]-NRT-code), using
- digital (7, 21, 98)-net over F32, using
(103−28, 103, 18725)-Net in Base 32 — Constructive
(75, 103, 18725)-net in base 32, using
- 1 times m-reduction [i] based on (75, 104, 18725)-net in base 32, using
- net defined by OOA [i] based on OOA(32104, 18725, S32, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(32104, 262151, S32, 29), using
- discarding factors based on OA(32104, 262152, S32, 29), using
- discarding parts of the base [i] based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 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 C([0,14]) ⊂ C([0,13]) [i] based on
- discarding parts of the base [i] based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- discarding factors based on OA(32104, 262152, S32, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(32104, 262151, S32, 29), using
- net defined by OOA [i] based on OOA(32104, 18725, S32, 29, 29), using
(103−28, 103, 194511)-Net over F32 — Digital
Digital (75, 103, 194511)-net over F32, using
(103−28, 103, large)-Net in Base 32 — Upper bound on s
There is no (75, 103, large)-net in base 32, because
- 26 times m-reduction [i] would yield (75, 77, large)-net in base 32, but