Best Known (22, 22+22, s)-Nets in Base 32
(22, 22+22, 162)-Net over F32 — Constructive and digital
Digital (22, 44, 162)-net over F32, using
- 2 times m-reduction [i] based on digital (22, 46, 162)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 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, 31, 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, 15, 64)-net over F32, using
- (u, u+v)-construction [i] based on
(22, 22+22, 261)-Net in Base 32 — Constructive
(22, 44, 261)-net in base 32, using
- 4 times m-reduction [i] based on (22, 48, 261)-net in base 32, using
- base change [i] based on digital (4, 30, 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, 30, 261)-net over F256, using
(22, 22+22, 515)-Net over F32 — Digital
Digital (22, 44, 515)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3244, 515, F32, 2, 22) (dual of [(515, 2), 986, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3244, 1030, F32, 22) (dual of [1030, 986, 23]-code), using
- construction XX applied to C1 = C([1021,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1021,19]) [i] based on
- linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3239, 1023, F32, 20) (dual of [1023, 984, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,19}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- 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 XX applied to C1 = C([1021,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([1021,19]) [i] based on
- OOA 2-folding [i] based on linear OA(3244, 1030, F32, 22) (dual of [1030, 986, 23]-code), using
(22, 22+22, 166049)-Net in Base 32 — Upper bound on s
There is no (22, 44, 166050)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1 685018 400844 914011 882943 860004 053381 222749 681159 259035 836447 656176 > 3244 [i]