Best Known (90−25, 90, s)-Nets in Base 32
(90−25, 90, 2806)-Net over F32 — Constructive and digital
Digital (65, 90, 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 (48, 73, 2730)-net over F32, using
- net defined by OOA [i] based on linear OOA(3273, 2730, F32, 25, 25) (dual of [(2730, 25), 68177, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3273, 32761, F32, 25) (dual of [32761, 32688, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3273, 32768, F32, 25) (dual of [32768, 32695, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3273, 32761, F32, 25) (dual of [32761, 32688, 26]-code), using
- net defined by OOA [i] based on linear OOA(3273, 2730, F32, 25, 25) (dual of [(2730, 25), 68177, 26]-NRT-code), using
- digital (5, 17, 76)-net over F32, using
(90−25, 90, 21846)-Net in Base 32 — Constructive
(65, 90, 21846)-net in base 32, using
- base change [i] based on digital (50, 75, 21846)-net over F64, using
- net defined by OOA [i] based on linear OOA(6475, 21846, F64, 25, 25) (dual of [(21846, 25), 546075, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6475, 262153, F64, 25) (dual of [262153, 262078, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6475, 262155, F64, 25) (dual of [262155, 262080, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(6475, 262155, F64, 25) (dual of [262155, 262080, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6475, 262153, F64, 25) (dual of [262153, 262078, 26]-code), using
- net defined by OOA [i] based on linear OOA(6475, 21846, F64, 25, 25) (dual of [(21846, 25), 546075, 26]-NRT-code), using
(90−25, 90, 139428)-Net over F32 — Digital
Digital (65, 90, 139428)-net over F32, using
(90−25, 90, large)-Net in Base 32 — Upper bound on s
There is no (65, 90, large)-net in base 32, because
- 23 times m-reduction [i] would yield (65, 67, large)-net in base 32, but