Best Known (37, 60, s)-Nets in Base 27
(37, 60, 256)-Net over F27 — Constructive and digital
Digital (37, 60, 256)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 7, 64)-net over F27, using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- digital (4, 11, 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 (4, 15, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 27, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (2, 7, 64)-net over F27, using
(37, 60, 596)-Net in Base 27 — Constructive
(37, 60, 596)-net in base 27, using
- base change [i] based on digital (22, 45, 596)-net over F81, using
- net defined by OOA [i] based on linear OOA(8145, 596, F81, 23, 23) (dual of [(596, 23), 13663, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8145, 6557, F81, 23) (dual of [6557, 6512, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8145, 6557, F81, 23) (dual of [6557, 6512, 24]-code), using
- net defined by OOA [i] based on linear OOA(8145, 596, F81, 23, 23) (dual of [(596, 23), 13663, 24]-NRT-code), using
(37, 60, 2801)-Net over F27 — Digital
Digital (37, 60, 2801)-net over F27, using
(37, 60, large)-Net in Base 27 — Upper bound on s
There is no (37, 60, large)-net in base 27, because
- 21 times m-reduction [i] would yield (37, 39, large)-net in base 27, but