Best Known (51, 51+22, s)-Nets in Base 32
(51, 51+22, 2982)-Net over F32 — Constructive and digital
Digital (51, 73, 2982)-net over F32, using
- net defined by OOA [i] based on linear OOA(3273, 2982, F32, 22, 22) (dual of [(2982, 22), 65531, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3273, 32802, F32, 22) (dual of [32802, 32729, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 32804, F32, 22) (dual of [32804, 32731, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(21) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3273, 32804, F32, 22) (dual of [32804, 32731, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3273, 32802, F32, 22) (dual of [32802, 32729, 23]-code), using
(51, 51+22, 5958)-Net in Base 32 — Constructive
(51, 73, 5958)-net in base 32, using
- t-expansion [i] based on (50, 73, 5958)-net in base 32, using
- net defined by OOA [i] based on OOA(3273, 5958, S32, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(3273, 65539, S32, 23), using
- 1 times code embedding in larger space [i] based on OA(3272, 65538, S32, 23), using
- discarding parts of the base [i] based on linear OA(25645, 65538, F256, 23) (dual of [65538, 65493, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(25645, 65538, F256, 23) (dual of [65538, 65493, 24]-code), using
- 1 times code embedding in larger space [i] based on OA(3272, 65538, S32, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(3273, 65539, S32, 23), using
- net defined by OOA [i] based on OOA(3273, 5958, S32, 23, 23), using
(51, 51+22, 47798)-Net over F32 — Digital
Digital (51, 73, 47798)-net over F32, using
(51, 51+22, large)-Net in Base 32 — Upper bound on s
There is no (51, 73, large)-net in base 32, because
- 20 times m-reduction [i] would yield (51, 53, large)-net in base 32, but