Best Known (55, 55+22, s)-Nets in Base 32
(55, 55+22, 3023)-Net over F32 — Constructive and digital
Digital (55, 77, 3023)-net over F32, using
- 321 times duplication [i] based on digital (54, 76, 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 (42, 64, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- 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(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(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(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
- digital (1, 12, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(55, 55+22, 23831)-Net in Base 32 — Constructive
(55, 77, 23831)-net in base 32, using
- net defined by OOA [i] based on OOA(3277, 23831, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3277, 262141, S32, 22), using
- discarding factors based on OA(3277, 262147, S32, 22), using
- discarding parts of the base [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(6464, 262147, F64, 22) (dual of [262147, 262083, 23]-code), using
- discarding factors based on OA(3277, 262147, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3277, 262141, S32, 22), using
(55, 55+22, 92483)-Net over F32 — Digital
Digital (55, 77, 92483)-net over F32, using
(55, 55+22, large)-Net in Base 32 — Upper bound on s
There is no (55, 77, large)-net in base 32, because
- 20 times m-reduction [i] would yield (55, 57, large)-net in base 32, but