Best Known (34, 34+21, s)-Nets in Base 27
(34, 34+21, 228)-Net over F27 — Constructive and digital
Digital (34, 55, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 12, 76)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 730)-net over F27, using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- digital (1, 8, 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 (1, 4, 730)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 27, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (5, 12, 76)-net over F27, using
(34, 34+21, 656)-Net in Base 27 — Constructive
(34, 55, 656)-net in base 27, using
- net defined by OOA [i] based on OOA(2755, 656, S27, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(2755, 6561, S27, 21), using
- discarding factors based on OA(2755, 6563, S27, 21), using
- discarding parts of the base [i] based on linear OA(8141, 6563, F81, 21) (dual of [6563, 6522, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(8141, 6563, F81, 21) (dual of [6563, 6522, 22]-code), using
- discarding factors based on OA(2755, 6563, S27, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(2755, 6561, S27, 21), using
(34, 34+21, 2768)-Net over F27 — Digital
Digital (34, 55, 2768)-net over F27, using
(34, 34+21, large)-Net in Base 27 — Upper bound on s
There is no (34, 55, large)-net in base 27, because
- 19 times m-reduction [i] would yield (34, 36, large)-net in base 27, but