Best Known (44, 60, s)-Nets in Base 32
(44, 60, 4195)-Net over F32 — Constructive and digital
Digital (44, 60, 4195)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- 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)
- generalized (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 (6, 14, 99)-net over F32, using
(44, 60, 32770)-Net in Base 32 — Constructive
(44, 60, 32770)-net in base 32, using
- base change [i] based on digital (34, 50, 32770)-net over F64, using
- net defined by OOA [i] based on linear OOA(6450, 32770, F64, 16, 16) (dual of [(32770, 16), 524270, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6450, 262160, F64, 16) (dual of [262160, 262110, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [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(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(6450, 262163, F64, 16) (dual of [262163, 262113, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(6450, 262160, F64, 16) (dual of [262160, 262110, 17]-code), using
- net defined by OOA [i] based on linear OOA(6450, 32770, F64, 16, 16) (dual of [(32770, 16), 524270, 17]-NRT-code), using
(44, 60, 217280)-Net over F32 — Digital
Digital (44, 60, 217280)-net over F32, using
(44, 60, large)-Net in Base 32 — Upper bound on s
There is no (44, 60, large)-net in base 32, because
- 14 times m-reduction [i] would yield (44, 46, large)-net in base 32, but