Best Known (30−14, 30, s)-Nets in Base 25
(30−14, 30, 132)-Net over F25 — Constructive and digital
Digital (16, 30, 132)-net over F25, using
- 2 times m-reduction [i] based on digital (16, 32, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 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 (4, 20, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 12, 66)-net over F25, using
- (u, u+v)-construction [i] based on
(30−14, 30, 521)-Net over F25 — Digital
Digital (16, 30, 521)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2530, 521, F25, 14) (dual of [521, 491, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2530, 636, F25, 14) (dual of [636, 606, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(2527, 625, F25, 14) (dual of [625, 598, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2530, 636, F25, 14) (dual of [636, 606, 15]-code), using
(30−14, 30, 137996)-Net in Base 25 — Upper bound on s
There is no (16, 30, 137997)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 867377 565662 877745 437461 471764 782567 823945 > 2530 [i]