Best Known (42, 59, s)-Nets in Base 32
(42, 59, 4140)-Net over F32 — Constructive and digital
Digital (42, 59, 4140)-net over F32, using
- 321 times duplication [i] based on digital (41, 58, 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 (32, 49, 4096)-net over F32, using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- digital (1, 9, 44)-net over F32, using
- (u, u+v)-construction [i] based on
(42, 59, 32768)-Net in Base 32 — Constructive
(42, 59, 32768)-net in base 32, using
- net defined by OOA [i] based on OOA(3259, 32768, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3259, 262145, S32, 17), using
- discarding factors based on OA(3259, 262147, S32, 17), using
- discarding parts of the base [i] based on linear OA(6449, 262147, F64, 17) (dual of [262147, 262098, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(6449, 262144, F64, 17) (dual of [262144, 262095, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(6449, 262147, F64, 17) (dual of [262147, 262098, 18]-code), using
- discarding factors based on OA(3259, 262147, S32, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3259, 262145, S32, 17), using
(42, 59, 77886)-Net over F32 — Digital
Digital (42, 59, 77886)-net over F32, using
(42, 59, large)-Net in Base 32 — Upper bound on s
There is no (42, 59, large)-net in base 32, because
- 15 times m-reduction [i] would yield (42, 44, large)-net in base 32, but