Best Known (38, 59, s)-Nets in Base 27
(38, 59, 280)-Net over F27 — Constructive and digital
Digital (38, 59, 280)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (0, 3, 28)-net over F27 (see above)
- digital (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 5, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 10, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 21, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
(38, 59, 657)-Net in Base 27 — Constructive
(38, 59, 657)-net in base 27, using
- net defined by OOA [i] based on OOA(2759, 657, S27, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(2759, 6571, S27, 21), using
- discarding factors based on OA(2759, 6573, S27, 21), using
- discarding parts of the base [i] based on linear OA(8144, 6573, F81, 21) (dual of [6573, 6529, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding parts of the base [i] based on linear OA(8144, 6573, F81, 21) (dual of [6573, 6529, 22]-code), using
- discarding factors based on OA(2759, 6573, S27, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(2759, 6571, S27, 21), using
(38, 59, 5342)-Net over F27 — Digital
Digital (38, 59, 5342)-net over F27, using
(38, 59, large)-Net in Base 27 — Upper bound on s
There is no (38, 59, large)-net in base 27, because
- 19 times m-reduction [i] would yield (38, 40, large)-net in base 27, but