Best Known (40, 58, s)-Nets in Base 32
(40, 58, 3643)-Net over F32 — Constructive and digital
Digital (40, 58, 3643)-net over F32, using
- 322 times duplication [i] based on digital (38, 56, 3643)-net over F32, using
- net defined by OOA [i] based on linear OOA(3256, 3643, F32, 18, 18) (dual of [(3643, 18), 65518, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3256, 32787, F32, 18) (dual of [32787, 32731, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(324, 19, F32, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- OA 9-folding and stacking [i] based on linear OA(3256, 32787, F32, 18) (dual of [32787, 32731, 19]-code), using
- net defined by OOA [i] based on linear OOA(3256, 3643, F32, 18, 18) (dual of [(3643, 18), 65518, 19]-NRT-code), using
(40, 58, 7282)-Net in Base 32 — Constructive
(40, 58, 7282)-net in base 32, using
- 322 times duplication [i] based on (38, 56, 7282)-net in base 32, using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
(40, 58, 32795)-Net over F32 — Digital
Digital (40, 58, 32795)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3258, 32795, F32, 18) (dual of [32795, 32737, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(3252, 32768, F32, 18) (dual of [32768, 32716, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(3231, 32768, F32, 11) (dual of [32768, 32737, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(326, 27, F32, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
(40, 58, large)-Net in Base 32 — Upper bound on s
There is no (40, 58, large)-net in base 32, because
- 16 times m-reduction [i] would yield (40, 42, large)-net in base 32, but