Best Known (55−16, 55, s)-Nets in Base 32
(55−16, 55, 4140)-Net over F32 — Constructive and digital
Digital (39, 55, 4140)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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 (30, 46, 4096)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 4096, F32, 16, 16) (dual of [(4096, 16), 65490, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on 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]
- OA 8-folding and stacking [i] based on linear OA(3246, 32768, F32, 16) (dual of [32768, 32722, 17]-code), using
- net defined by OOA [i] based on linear OOA(3246, 4096, F32, 16, 16) (dual of [(4096, 16), 65490, 17]-NRT-code), using
- digital (1, 9, 44)-net over F32, using
(55−16, 55, 8193)-Net in Base 32 — Constructive
(39, 55, 8193)-net in base 32, using
- 321 times duplication [i] based on (38, 54, 8193)-net in base 32, using
- base change [i] based on (29, 45, 8193)-net in base 64, using
- 641 times duplication [i] based on (28, 44, 8193)-net in base 64, using
- base change [i] based on digital (17, 33, 8193)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 8193, F256, 16, 16) (dual of [(8193, 16), 131055, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(25633, 65544, F256, 16) (dual of [65544, 65511, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- 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(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- OA 8-folding and stacking [i] based on linear OA(25633, 65544, F256, 16) (dual of [65544, 65511, 17]-code), using
- net defined by OOA [i] based on linear OOA(25633, 8193, F256, 16, 16) (dual of [(8193, 16), 131055, 17]-NRT-code), using
- base change [i] based on digital (17, 33, 8193)-net over F256, using
- 641 times duplication [i] based on (28, 44, 8193)-net in base 64, using
- base change [i] based on (29, 45, 8193)-net in base 64, using
(55−16, 55, 68444)-Net over F32 — Digital
Digital (39, 55, 68444)-net over F32, using
(55−16, 55, large)-Net in Base 32 — Upper bound on s
There is no (39, 55, large)-net in base 32, because
- 14 times m-reduction [i] would yield (39, 41, large)-net in base 32, but