Best Known (75, 103, s)-Nets in Base 25
(75, 103, 1242)-Net over F25 — Constructive and digital
Digital (75, 103, 1242)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 24, 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 (51, 79, 1116)-net over F25, using
- net defined by OOA [i] based on linear OOA(2579, 1116, F25, 28, 28) (dual of [(1116, 28), 31169, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2579, 15624, F25, 28) (dual of [15624, 15545, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2579, 15624, F25, 28) (dual of [15624, 15545, 29]-code), using
- net defined by OOA [i] based on linear OOA(2579, 1116, F25, 28, 28) (dual of [(1116, 28), 31169, 29]-NRT-code), using
- digital (10, 24, 126)-net over F25, using
(75, 103, 97980)-Net over F25 — Digital
Digital (75, 103, 97980)-net over F25, using
(75, 103, large)-Net in Base 25 — Upper bound on s
There is no (75, 103, large)-net in base 25, because
- 26 times m-reduction [i] would yield (75, 77, large)-net in base 25, but