Best Known (52, 73, s)-Nets in Base 32
(52, 73, 3321)-Net over F32 — Constructive and digital
Digital (52, 73, 3321)-net over F32, using
- 321 times duplication [i] based on digital (51, 72, 3321)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (40, 61, 3277)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 3277, F32, 21, 21) (dual of [(3277, 21), 68756, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3261, 32771, F32, 21) (dual of [32771, 32710, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(3261, 32771, F32, 21) (dual of [32771, 32710, 22]-code), using
- net defined by OOA [i] based on linear OOA(3261, 3277, F32, 21, 21) (dual of [(3277, 21), 68756, 22]-NRT-code), using
- digital (1, 11, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(52, 73, 6555)-Net in Base 32 — Constructive
(52, 73, 6555)-net in base 32, using
- net defined by OOA [i] based on OOA(3273, 6555, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3273, 65551, S32, 21), using
- 1 times code embedding in larger space [i] based on OA(3272, 65550, S32, 21), using
- discarding parts of the base [i] based on linear OA(25645, 65550, F256, 21) (dual of [65550, 65505, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(25645, 65550, F256, 21) (dual of [65550, 65505, 22]-code), using
- 1 times code embedding in larger space [i] based on OA(3272, 65550, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3273, 65551, S32, 21), using
(52, 73, 83521)-Net over F32 — Digital
Digital (52, 73, 83521)-net over F32, using
(52, 73, large)-Net in Base 32 — Upper bound on s
There is no (52, 73, large)-net in base 32, because
- 19 times m-reduction [i] would yield (52, 54, large)-net in base 32, but