Best Known (43−22, 43, s)-Nets in Base 32
(43−22, 43, 162)-Net over F32 — Constructive and digital
Digital (21, 43, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (7, 29, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (3, 14, 64)-net over F32, using
(43−22, 43, 261)-Net in Base 32 — Constructive
(21, 43, 261)-net in base 32, using
- 321 times duplication [i] based on (20, 42, 261)-net in base 32, using
- base change [i] based on (13, 35, 261)-net in base 64, using
- 1 times m-reduction [i] based on (13, 36, 261)-net in base 64, using
- base change [i] based on digital (4, 27, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 27, 261)-net over F256, using
- 1 times m-reduction [i] based on (13, 36, 261)-net in base 64, using
- base change [i] based on (13, 35, 261)-net in base 64, using
(43−22, 43, 444)-Net over F32 — Digital
Digital (21, 43, 444)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 444, F32, 2, 22) (dual of [(444, 2), 845, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 513, F32, 2, 22) (dual of [(513, 2), 983, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3243, 1026, F32, 22) (dual of [1026, 983, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(3243, 1024, F32, 22) (dual of [1024, 981, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3241, 1024, F32, 21) (dual of [1024, 983, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(3243, 1026, F32, 22) (dual of [1026, 983, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 513, F32, 2, 22) (dual of [(513, 2), 983, 23]-NRT-code), using
(43−22, 43, 121171)-Net in Base 32 — Upper bound on s
There is no (21, 43, 121172)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 52657 357508 697693 955031 718208 021810 634256 597407 128722 080765 085578 > 3243 [i]