Best Known (93−32, 93, s)-Nets in Base 32
(93−32, 93, 2047)-Net over F32 — Constructive and digital
Digital (61, 93, 2047)-net over F32, using
- net defined by OOA [i] based on linear OOA(3293, 2047, F32, 32, 32) (dual of [(2047, 32), 65411, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(3293, 32752, F32, 32) (dual of [32752, 32659, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 32767, F32, 32) (dual of [32767, 32674, 33]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 32767, F32, 32) (dual of [32767, 32674, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(3293, 32752, F32, 32) (dual of [32752, 32659, 33]-code), using
(93−32, 93, 16383)-Net over F32 — Digital
Digital (61, 93, 16383)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3293, 16383, F32, 2, 32) (dual of [(16383, 2), 32673, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3293, 32766, F32, 32) (dual of [32766, 32673, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 32767, F32, 32) (dual of [32767, 32674, 33]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 32767, F32, 32) (dual of [32767, 32674, 33]-code), using
- OOA 2-folding [i] based on linear OA(3293, 32766, F32, 32) (dual of [32766, 32673, 33]-code), using
(93−32, 93, large)-Net in Base 32 — Upper bound on s
There is no (61, 93, large)-net in base 32, because
- 30 times m-reduction [i] would yield (61, 63, large)-net in base 32, but