Best Known (67, 103, s)-Nets in Base 32
(67, 103, 1820)-Net over F32 — Constructive and digital
Digital (67, 103, 1820)-net over F32, using
- net defined by OOA [i] based on linear OOA(32103, 1820, F32, 36, 36) (dual of [(1820, 36), 65417, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(32103, 32760, F32, 36) (dual of [32760, 32657, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(32103, 32760, F32, 36) (dual of [32760, 32657, 37]-code), using
(67, 103, 16385)-Net over F32 — Digital
Digital (67, 103, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(32103, 16385, F32, 2, 36) (dual of [(16385, 2), 32667, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32103, 32770, F32, 36) (dual of [32770, 32667, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32103, 32771, F32, 36) (dual of [32771, 32668, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- discarding factors / shortening the dual code based on linear OA(32103, 32771, F32, 36) (dual of [32771, 32668, 37]-code), using
- OOA 2-folding [i] based on linear OA(32103, 32770, F32, 36) (dual of [32770, 32667, 37]-code), using
(67, 103, large)-Net in Base 32 — Upper bound on s
There is no (67, 103, large)-net in base 32, because
- 34 times m-reduction [i] would yield (67, 69, large)-net in base 32, but