Best Known (22−10, 22, s)-Nets in Base 25
(22−10, 22, 132)-Net over F25 — Constructive and digital
Digital (12, 22, 132)-net over F25, using
- t-expansion [i] based on digital (11, 22, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 300)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), using
- net defined by OOA [i] based on linear OOA(257, 300, F25, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
- digital (4, 15, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- digital (2, 7, 300)-net over F25, using
- (u, u+v)-construction [i] based on
(22−10, 22, 652)-Net over F25 — Digital
Digital (12, 22, 652)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2522, 652, F25, 10) (dual of [652, 630, 11]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 17 times 0) [i] based on linear OA(2519, 628, F25, 10) (dual of [628, 609, 11]-code), using
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,7]), C2 = C([0,8]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C([623,8]) [i] based on
- 21 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 17 times 0) [i] based on linear OA(2519, 628, F25, 10) (dual of [628, 609, 11]-code), using
(22−10, 22, 153657)-Net in Base 25 — Upper bound on s
There is no (12, 22, 153658)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 5 684366 230424 677651 709469 801649 > 2522 [i]