Best Known (57, 80, s)-Nets in Base 32
(57, 80, 3023)-Net over F32 — Constructive and digital
Digital (57, 80, 3023)-net over F32, using
- 321 times duplication [i] based on digital (56, 79, 3023)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (44, 67, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
- digital (1, 12, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(57, 80, 5959)-Net in Base 32 — Constructive
(57, 80, 5959)-net in base 32, using
- base change [i] based on digital (27, 50, 5959)-net over F256, using
- 2561 times duplication [i] based on digital (26, 49, 5959)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 5959, F256, 23, 23) (dual of [(5959, 23), 137008, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [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(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(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(22) ⊂ Ce(17) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(25649, 65550, F256, 23) (dual of [65550, 65501, 24]-code), using
- net defined by OOA [i] based on linear OOA(25649, 5959, F256, 23, 23) (dual of [(5959, 23), 137008, 24]-NRT-code), using
- 2561 times duplication [i] based on digital (26, 49, 5959)-net over F256, using
(57, 80, 86860)-Net over F32 — Digital
Digital (57, 80, 86860)-net over F32, using
(57, 80, large)-Net in Base 32 — Upper bound on s
There is no (57, 80, large)-net in base 32, because
- 21 times m-reduction [i] would yield (57, 59, large)-net in base 32, but