Best Known (54, 78, s)-Nets in Base 32
(54, 78, 2733)-Net over F32 — Constructive and digital
Digital (54, 78, 2733)-net over F32, using
- 321 times duplication [i] based on digital (53, 77, 2733)-net over F32, using
- net defined by OOA [i] based on linear OOA(3277, 2733, F32, 24, 24) (dual of [(2733, 24), 65515, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3277, 32796, F32, 24) (dual of [32796, 32719, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3277, 32799, F32, 24) (dual of [32799, 32722, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- 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(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(327, 31, F32, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3277, 32799, F32, 24) (dual of [32799, 32722, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3277, 32796, F32, 24) (dual of [32796, 32719, 25]-code), using
- net defined by OOA [i] based on linear OOA(3277, 2733, F32, 24, 24) (dual of [(2733, 24), 65515, 25]-NRT-code), using
(54, 78, 5461)-Net in Base 32 — Constructive
(54, 78, 5461)-net in base 32, using
- base change [i] based on (41, 65, 5461)-net in base 64, using
- 1 times m-reduction [i] based on (41, 66, 5461)-net in base 64, using
- net defined by OOA [i] based on OOA(6466, 5461, S64, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6466, 65533, S64, 25), using
- discarding factors based on OA(6466, 65538, S64, 25), using
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(25649, 65538, F256, 25) (dual of [65538, 65489, 26]-code), using
- discarding factors based on OA(6466, 65538, S64, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(6466, 65533, S64, 25), using
- net defined by OOA [i] based on OOA(6466, 5461, S64, 25, 25), using
- 1 times m-reduction [i] based on (41, 66, 5461)-net in base 64, using
(54, 78, 38694)-Net over F32 — Digital
Digital (54, 78, 38694)-net over F32, using
(54, 78, large)-Net in Base 32 — Upper bound on s
There is no (54, 78, large)-net in base 32, because
- 22 times m-reduction [i] would yield (54, 56, large)-net in base 32, but