Best Known (71−35, 71, s)-Nets in Base 25
(71−35, 71, 230)-Net over F25 — Constructive and digital
Digital (36, 71, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 26, 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 (10, 45, 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 (9, 26, 104)-net over F25, using
(71−35, 71, 492)-Net over F25 — Digital
Digital (36, 71, 492)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2571, 492, F25, 35) (dual of [492, 421, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, 642, F25, 35) (dual of [642, 571, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2566, 625, F25, 35) (dual of [625, 559, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2554, 625, F25, 29) (dual of [625, 571, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(255, 17, F25, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2571, 642, F25, 35) (dual of [642, 571, 36]-code), using
(71−35, 71, 170582)-Net in Base 25 — Upper bound on s
There is no (36, 71, 170583)-net in base 25, because
- 1 times m-reduction [i] would yield (36, 70, 170583)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 71 747570 683634 781415 203505 104906 031649 601267 874693 956279 142366 874645 848865 791855 028400 886600 721065 > 2570 [i]