Best Known (39, 75, s)-Nets in Base 25
(39, 75, 252)-Net over F25 — Constructive and digital
Digital (39, 75, 252)-net over F25, using
- 2 times m-reduction [i] based on digital (39, 77, 252)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 29, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (10, 48, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- digital (10, 29, 126)-net over F25, using
- (u, u+v)-construction [i] based on
(39, 75, 606)-Net over F25 — Digital
Digital (39, 75, 606)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2575, 606, F25, 36) (dual of [606, 531, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2575, 648, F25, 36) (dual of [648, 573, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- linear OA(2568, 625, F25, 36) (dual of [625, 557, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2552, 625, F25, 28) (dual of [625, 573, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(257, 23, F25, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2575, 648, F25, 36) (dual of [648, 573, 37]-code), using
(39, 75, 210208)-Net in Base 25 — Upper bound on s
There is no (39, 75, 210209)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 700 694683 403696 012106 104184 420656 994897 875127 377821 096122 941745 060831 790977 512556 644590 130672 239409 843185 > 2575 [i]