Best Known (106−28, 106, s)-Nets in Base 32
(106−28, 106, 2445)-Net over F32 — Constructive and digital
Digital (78, 106, 2445)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (55, 83, 2341)-net over F32, using
- net defined by OOA [i] based on linear OOA(3283, 2341, F32, 28, 28) (dual of [(2341, 28), 65465, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] 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]
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
- net defined by OOA [i] based on linear OOA(3283, 2341, F32, 28, 28) (dual of [(2341, 28), 65465, 29]-NRT-code), using
- digital (9, 23, 104)-net over F32, using
(106−28, 106, 18726)-Net in Base 32 — Constructive
(78, 106, 18726)-net in base 32, using
- 321 times duplication [i] based on (77, 105, 18726)-net in base 32, using
- net defined by OOA [i] based on OOA(32105, 18726, S32, 28, 28), using
- OA 14-folding and stacking [i] based on OA(32105, 262164, S32, 28), using
- discarding factors based on OA(32105, 262167, S32, 28), using
- discarding parts of the base [i] based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(645, 23, F64, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(6487, 262167, F64, 28) (dual of [262167, 262080, 29]-code), using
- discarding factors based on OA(32105, 262167, S32, 28), using
- OA 14-folding and stacking [i] based on OA(32105, 262164, S32, 28), using
- net defined by OOA [i] based on OOA(32105, 18726, S32, 28, 28), using
(106−28, 106, 285873)-Net over F32 — Digital
Digital (78, 106, 285873)-net over F32, using
(106−28, 106, large)-Net in Base 32 — Upper bound on s
There is no (78, 106, large)-net in base 32, because
- 26 times m-reduction [i] would yield (78, 80, large)-net in base 32, but