Best Known (57, 73, s)-Nets in Base 32
(57, 73, 131138)-Net over F32 — Constructive and digital
Digital (57, 73, 131138)-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 (45, 61, 131072)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 131072, F32, 16, 16) (dual of [(131072, 16), 2097091, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using
- net defined by OOA [i] based on linear OOA(3261, 131072, F32, 16, 16) (dual of [(131072, 16), 2097091, 17]-NRT-code), using
- digital (4, 12, 66)-net over F32, using
(57, 73, 262177)-Net in Base 32 — Constructive
(57, 73, 262177)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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
- (49, 65, 262144)-net in base 32, using
- net defined by OOA [i] based on OOA(3265, 262144, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3265, 2097152, S32, 16), using
- discarding factors based on OA(3265, 2097155, S32, 16), using
- discarding parts of the base [i] based on linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using
- discarding factors based on OA(3265, 2097155, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3265, 2097152, S32, 16), using
- net defined by OOA [i] based on OOA(3265, 262144, S32, 16, 16), using
- digital (0, 8, 33)-net over F32, using
(57, 73, 4379948)-Net over F32 — Digital
Digital (57, 73, 4379948)-net over F32, using
(57, 73, large)-Net in Base 32 — Upper bound on s
There is no (57, 73, large)-net in base 32, because
- 14 times m-reduction [i] would yield (57, 59, large)-net in base 32, but