Best Known (63, 63+28, s)-Nets in Base 32
(63, 63+28, 2343)-Net over F32 — Constructive and digital
Digital (63, 91, 2343)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 2343, F32, 28, 28) (dual of [(2343, 28), 65513, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3291, 32802, F32, 28) (dual of [32802, 32711, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, 32804, F32, 28) (dual of [32804, 32713, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3255, 32768, F32, 19) (dual of [32768, 32713, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(329, 36, F32, 8) (dual of [36, 27, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(329, 43, F32, 8) (dual of [43, 34, 9]-code), using
- algebraic-geometric code AG(F,34P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- discarding factors / shortening the dual code based on linear OA(329, 43, F32, 8) (dual of [43, 34, 9]-code), using
- construction X applied to Ce(27) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3291, 32804, F32, 28) (dual of [32804, 32713, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3291, 32802, F32, 28) (dual of [32802, 32711, 29]-code), using
(63, 63+28, 4681)-Net in Base 32 — Constructive
(63, 91, 4681)-net in base 32, using
- 1 times m-reduction [i] based on (63, 92, 4681)-net in base 32, using
- net defined by OOA [i] based on OOA(3292, 4681, S32, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3292, 65535, S32, 29), using
- discarding factors based on OA(3292, 65538, S32, 29), using
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- discarding factors based on OA(3292, 65538, S32, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3292, 65535, S32, 29), using
- net defined by OOA [i] based on OOA(3292, 4681, S32, 29, 29), using
(63, 63+28, 41696)-Net over F32 — Digital
Digital (63, 91, 41696)-net over F32, using
(63, 63+28, large)-Net in Base 32 — Upper bound on s
There is no (63, 91, large)-net in base 32, because
- 26 times m-reduction [i] would yield (63, 65, large)-net in base 32, but