Best Known (66, 101, s)-Nets in Base 32
(66, 101, 1927)-Net over F32 — Constructive and digital
Digital (66, 101, 1927)-net over F32, using
- 321 times duplication [i] based on digital (65, 100, 1927)-net over F32, using
- net defined by OOA [i] based on linear OOA(32100, 1927, F32, 35, 35) (dual of [(1927, 35), 67345, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
- net defined by OOA [i] based on linear OOA(32100, 1927, F32, 35, 35) (dual of [(1927, 35), 67345, 36]-NRT-code), using
(66, 101, 16387)-Net over F32 — Digital
Digital (66, 101, 16387)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(32101, 16387, F32, 2, 35) (dual of [(16387, 2), 32673, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32101, 32774, F32, 35) (dual of [32774, 32673, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, 32775, F32, 35) (dual of [32775, 32674, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(32) [i] based on
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(34) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(32101, 32775, F32, 35) (dual of [32775, 32674, 36]-code), using
- OOA 2-folding [i] based on linear OA(32101, 32774, F32, 35) (dual of [32774, 32673, 36]-code), using
(66, 101, large)-Net in Base 32 — Upper bound on s
There is no (66, 101, large)-net in base 32, because
- 33 times m-reduction [i] would yield (66, 68, large)-net in base 32, but