Best Known (21, 21+13, s)-Nets in Base 27
(21, 21+13, 280)-Net over F27 — Constructive and digital
Digital (21, 34, 280)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27, using
- 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, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 13, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 1, 28)-net over F27, using
(21, 21+13, 1093)-Net in Base 27 — Constructive
(21, 34, 1093)-net in base 27, using
- net defined by OOA [i] based on OOA(2734, 1093, S27, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(2734, 6559, S27, 13), using
- discarding factors based on OA(2734, 6563, S27, 13), using
- discarding parts of the base [i] based on linear OA(8125, 6563, F81, 13) (dual of [6563, 6538, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(8125, 6561, F81, 13) (dual of [6561, 6536, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(8125, 6563, F81, 13) (dual of [6563, 6538, 14]-code), using
- discarding factors based on OA(2734, 6563, S27, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(2734, 6559, S27, 13), using
(21, 21+13, 2318)-Net over F27 — Digital
Digital (21, 34, 2318)-net over F27, using
(21, 21+13, large)-Net in Base 27 — Upper bound on s
There is no (21, 34, large)-net in base 27, because
- 11 times m-reduction [i] would yield (21, 23, large)-net in base 27, but