Best Known (50, 50+20, s)-Nets in Base 27
(50, 50+20, 2016)-Net over F27 — Constructive and digital
Digital (50, 70, 2016)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (38, 58, 1968)-net over F27, using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- digital (2, 12, 48)-net over F27, using
(50, 50+20, 57248)-Net over F27 — Digital
Digital (50, 70, 57248)-net over F27, using
(50, 50+20, large)-Net in Base 27 — Upper bound on s
There is no (50, 70, large)-net in base 27, because
- 18 times m-reduction [i] would yield (50, 52, large)-net in base 27, but