Best Known (58−16, 58, s)-Nets in Base 32
(58−16, 58, 4162)-Net over F32 — Constructive and digital
Digital (42, 58, 4162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 66)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (4, 12, 66)-net over F32, using
(58−16, 58, 32769)-Net in Base 32 — Constructive
(42, 58, 32769)-net in base 32, using
- net defined by OOA [i] based on OOA(3258, 32769, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3258, 262152, S32, 16), using
- discarding factors based on OA(3258, 262155, S32, 16), using
- discarding parts of the base [i] based on linear OA(6448, 262155, F64, 16) (dual of [262155, 262107, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- discarding parts of the base [i] based on linear OA(6448, 262155, F64, 16) (dual of [262155, 262107, 17]-code), using
- discarding factors based on OA(3258, 262155, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3258, 262152, S32, 16), using
(58−16, 58, 136881)-Net over F32 — Digital
Digital (42, 58, 136881)-net over F32, using
(58−16, 58, large)-Net in Base 32 — Upper bound on s
There is no (42, 58, large)-net in base 32, because
- 14 times m-reduction [i] would yield (42, 44, large)-net in base 32, but