Best Known (87−24, 87, s)-Nets in Base 32
(87−24, 87, 2806)-Net over F32 — Constructive and digital
Digital (63, 87, 2806)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (46, 70, 2730)-net over F32, using
- net defined by OOA [i] based on linear OOA(3270, 2730, F32, 24, 24) (dual of [(2730, 24), 65450, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3270, 32760, F32, 24) (dual of [32760, 32690, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3270, 32760, F32, 24) (dual of [32760, 32690, 25]-code), using
- net defined by OOA [i] based on linear OOA(3270, 2730, F32, 24, 24) (dual of [(2730, 24), 65450, 25]-NRT-code), using
- digital (5, 17, 76)-net over F32, using
(87−24, 87, 21846)-Net in Base 32 — Constructive
(63, 87, 21846)-net in base 32, using
- net defined by OOA [i] based on OOA(3287, 21846, S32, 24, 24), using
- OA 12-folding and stacking [i] based on OA(3287, 262152, S32, 24), using
- discarding factors based on OA(3287, 262155, S32, 24), using
- discarding parts of the base [i] based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- discarding factors based on OA(3287, 262155, S32, 24), using
- OA 12-folding and stacking [i] based on OA(3287, 262152, S32, 24), using
(87−24, 87, 150149)-Net over F32 — Digital
Digital (63, 87, 150149)-net over F32, using
(87−24, 87, large)-Net in Base 32 — Upper bound on s
There is no (63, 87, large)-net in base 32, because
- 22 times m-reduction [i] would yield (63, 65, large)-net in base 32, but