Best Known (21−10, 21, s)-Nets in Base 25
(21−10, 21, 132)-Net over F25 — Constructive and digital
Digital (11, 21, 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, 14, 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
(21−10, 21, 487)-Net over F25 — Digital
Digital (11, 21, 487)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2521, 487, F25, 10) (dual of [487, 466, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2521, 633, F25, 10) (dual of [633, 612, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(2519, 625, F25, 10) (dual of [625, 606, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2513, 625, F25, 7) (dual of [625, 612, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(2521, 633, F25, 10) (dual of [633, 612, 11]-code), using
(21−10, 21, 80716)-Net in Base 25 — Upper bound on s
There is no (11, 21, 80717)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 227383 753480 814241 459851 755417 > 2521 [i]