Best Known (20, 29, s)-Nets in Base 25
(20, 29, 3932)-Net over F25 — Constructive and digital
Digital (20, 29, 3932)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 26)-net over F25, using
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using
- the rational function field F25(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 25)-sequence over F25, using
- digital (16, 25, 3906)-net over F25, using
- net defined by OOA [i] based on linear OOA(2525, 3906, F25, 9, 9) (dual of [(3906, 9), 35129, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2525, 15625, F25, 9) (dual of [15625, 15600, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(2525, 15625, F25, 9) (dual of [15625, 15600, 10]-code), using
- net defined by OOA [i] based on linear OOA(2525, 3906, F25, 9, 9) (dual of [(3906, 9), 35129, 10]-NRT-code), using
- digital (0, 4, 26)-net over F25, using
(20, 29, 18328)-Net over F25 — Digital
Digital (20, 29, 18328)-net over F25, using
(20, 29, large)-Net in Base 25 — Upper bound on s
There is no (20, 29, large)-net in base 25, because
- 7 times m-reduction [i] would yield (20, 22, large)-net in base 25, but