Best Known (59, 59+24, s)-Nets in Base 27
(59, 59+24, 1678)-Net over F27 — Constructive and digital
Digital (59, 83, 1678)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (46, 70, 1640)-net over F27, using
- net defined by OOA [i] based on linear OOA(2770, 1640, F27, 24, 24) (dual of [(1640, 24), 39290, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
- net defined by OOA [i] based on linear OOA(2770, 1640, F27, 24, 24) (dual of [(1640, 24), 39290, 25]-NRT-code), using
- digital (1, 13, 38)-net over F27, using
(59, 59+24, 53080)-Net over F27 — Digital
Digital (59, 83, 53080)-net over F27, using
(59, 59+24, large)-Net in Base 27 — Upper bound on s
There is no (59, 83, large)-net in base 27, because
- 22 times m-reduction [i] would yield (59, 61, large)-net in base 27, but