Best Known (21, 39, s)-Nets in Base 25
(21, 39, 156)-Net over F25 — Constructive and digital
Digital (21, 39, 156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (9, 27, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (3, 12, 52)-net over F25, using
(21, 39, 585)-Net over F25 — Digital
Digital (21, 39, 585)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2539, 585, F25, 18) (dual of [585, 546, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2539, 639, F25, 18) (dual of [639, 600, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(2535, 625, F25, 18) (dual of [625, 590, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2525, 625, F25, 13) (dual of [625, 600, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2539, 639, F25, 18) (dual of [639, 600, 19]-code), using
(21, 39, 197365)-Net in Base 25 — Upper bound on s
There is no (21, 39, 197366)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 3 308840 542739 478478 985662 382244 281526 125121 133479 705745 > 2539 [i]