Best Known (107−30, 107, s)-Nets in Base 32
(107−30, 107, 2249)-Net over F32 — Constructive and digital
Digital (77, 107, 2249)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (59, 89, 2185)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 2185, F32, 30, 30) (dual of [(2185, 30), 65461, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- 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(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(29) ⊂ Ce(27) [i] based on
- OA 15-folding and stacking [i] based on linear OA(3289, 32775, F32, 30) (dual of [32775, 32686, 31]-code), using
- net defined by OOA [i] based on linear OOA(3289, 2185, F32, 30, 30) (dual of [(2185, 30), 65461, 31]-NRT-code), using
- digital (3, 18, 64)-net over F32, using
(107−30, 107, 17476)-Net in Base 32 — Constructive
(77, 107, 17476)-net in base 32, using
- 321 times duplication [i] based on (76, 106, 17476)-net in base 32, using
- net defined by OOA [i] based on OOA(32106, 17476, S32, 30, 30), using
- OA 15-folding and stacking [i] based on OA(32106, 262140, S32, 30), using
- discarding factors based on OA(32106, 262147, S32, 30), using
- discarding parts of the base [i] based on linear OA(6488, 262147, F64, 30) (dual of [262147, 262059, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(6488, 262144, F64, 30) (dual of [262144, 262056, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(6485, 262144, F64, 29) (dual of [262144, 262059, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 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(29) ⊂ Ce(28) [i] based on
- discarding parts of the base [i] based on linear OA(6488, 262147, F64, 30) (dual of [262147, 262059, 31]-code), using
- discarding factors based on OA(32106, 262147, S32, 30), using
- OA 15-folding and stacking [i] based on OA(32106, 262140, S32, 30), using
- net defined by OOA [i] based on OOA(32106, 17476, S32, 30, 30), using
(107−30, 107, 134676)-Net over F32 — Digital
Digital (77, 107, 134676)-net over F32, using
(107−30, 107, large)-Net in Base 32 — Upper bound on s
There is no (77, 107, large)-net in base 32, because
- 28 times m-reduction [i] would yield (77, 79, large)-net in base 32, but