Best Known (40, 40+16, s)-Nets in Base 32
(40, 40+16, 4140)-Net over F32 — Constructive and digital
Digital (40, 56, 4140)-net over F32, using
- 321 times duplication [i] based on digital (39, 55, 4140)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 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 (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 (1, 9, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(40, 40+16, 32768)-Net in Base 32 — Constructive
(40, 56, 32768)-net in base 32, using
- net defined by OOA [i] based on OOA(3256, 32768, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3256, 262144, S32, 16), using
- discarding factors based on OA(3256, 262147, S32, 16), using
- discarding parts of the base [i] based on linear OA(6446, 262147, F64, 16) (dual of [262147, 262101, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [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(6443, 262144, F64, 15) (dual of [262144, 262101, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(6446, 262147, F64, 16) (dual of [262147, 262101, 17]-code), using
- discarding factors based on OA(3256, 262147, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3256, 262144, S32, 16), using
(40, 40+16, 86232)-Net over F32 — Digital
Digital (40, 56, 86232)-net over F32, using
(40, 40+16, large)-Net in Base 32 — Upper bound on s
There is no (40, 56, large)-net in base 32, because
- 14 times m-reduction [i] would yield (40, 42, large)-net in base 32, but