Best Known (61−17, 61, s)-Nets in Base 27
(61−17, 61, 2524)-Net over F27 — Constructive and digital
Digital (44, 61, 2524)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (32, 49, 2460)-net over F27, using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- digital (4, 12, 64)-net over F27, using
(61−17, 61, 2560)-Net in Base 27 — Constructive
(44, 61, 2560)-net in base 27, using
- (u, u+v)-construction [i] based on
- (4, 12, 100)-net in base 27, using
- base change [i] based on digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 9, 100)-net over F81, using
- digital (32, 49, 2460)-net over F27, using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2749, 19681, F27, 17) (dual of [19681, 19632, 18]-code), using
- net defined by OOA [i] based on linear OOA(2749, 2460, F27, 17, 17) (dual of [(2460, 17), 41771, 18]-NRT-code), using
- (4, 12, 100)-net in base 27, using
(61−17, 61, 74935)-Net over F27 — Digital
Digital (44, 61, 74935)-net over F27, using
(61−17, 61, large)-Net in Base 27 — Upper bound on s
There is no (44, 61, large)-net in base 27, because
- 15 times m-reduction [i] would yield (44, 46, large)-net in base 27, but