Best Known (59, 81, s)-Nets in Base 32
(59, 81, 3056)-Net over F32 — Constructive and digital
Digital (59, 81, 3056)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- 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 (0, 5, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (6, 17, 77)-net over F32, using
(59, 81, 23832)-Net in Base 32 — Constructive
(59, 81, 23832)-net in base 32, using
- 322 times duplication [i] based on (57, 79, 23832)-net in base 32, using
- net defined by OOA [i] based on OOA(3279, 23832, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3279, 262152, S32, 22), using
- 1 times code embedding in larger space [i] based on OA(3278, 262151, S32, 22), using
- discarding parts of the base [i] based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [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(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(6465, 262151, F64, 22) (dual of [262151, 262086, 23]-code), using
- 1 times code embedding in larger space [i] based on OA(3278, 262151, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3279, 262152, S32, 22), using
- net defined by OOA [i] based on OOA(3279, 23832, S32, 22, 22), using
(59, 81, 178951)-Net over F32 — Digital
Digital (59, 81, 178951)-net over F32, using
(59, 81, large)-Net in Base 32 — Upper bound on s
There is no (59, 81, large)-net in base 32, because
- 20 times m-reduction [i] would yield (59, 61, large)-net in base 32, but