Best Known (104−36, 104, s)-Nets in Base 32
(104−36, 104, 1820)-Net over F32 — Constructive and digital
Digital (68, 104, 1820)-net over F32, using
- 321 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(32103, 1820, F32, 36, 36) (dual of [(1820, 36), 65417, 37]-NRT-code), using
(104−36, 104, 16387)-Net over F32 — Digital
Digital (68, 104, 16387)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(32104, 16387, F32, 2, 36) (dual of [(16387, 2), 32670, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32104, 32774, F32, 36) (dual of [32774, 32670, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32104, 32775, F32, 36) (dual of [32775, 32671, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(33) [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(3297, 32768, F32, 34) (dual of [32768, 32671, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(35) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(32104, 32775, F32, 36) (dual of [32775, 32671, 37]-code), using
- OOA 2-folding [i] based on linear OA(32104, 32774, F32, 36) (dual of [32774, 32670, 37]-code), using
(104−36, 104, large)-Net in Base 32 — Upper bound on s
There is no (68, 104, large)-net in base 32, because
- 34 times m-reduction [i] would yield (68, 70, large)-net in base 32, but