Best Known (70, 70+33, s)-Nets in Base 32
(70, 70+33, 2050)-Net over F32 — Constructive and digital
Digital (70, 103, 2050)-net over F32, using
- net defined by OOA [i] based on linear OOA(32103, 2050, F32, 33, 33) (dual of [(2050, 33), 67547, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(32103, 32801, F32, 33) (dual of [32801, 32698, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(32103, 32802, F32, 33) (dual of [32802, 32699, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- 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(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- linear OA(320, 1, F32, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(32103, 32802, F32, 33) (dual of [32802, 32699, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(32103, 32801, F32, 33) (dual of [32801, 32698, 34]-code), using
(70, 70+33, 32802)-Net over F32 — Digital
Digital (70, 103, 32802)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32103, 32802, F32, 33) (dual of [32802, 32699, 34]-code), using
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
- 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(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- linear OA(320, 1, F32, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(32) ⊂ Ce(23) ⊂ Ce(22) [i] based on
(70, 70+33, large)-Net in Base 32 — Upper bound on s
There is no (70, 103, large)-net in base 32, because
- 31 times m-reduction [i] would yield (70, 72, large)-net in base 32, but