Best Known (44, 44+27, s)-Nets in Base 27
(44, 44+27, 256)-Net over F27 — Constructive and digital
Digital (44, 71, 256)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 10, 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, 13, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 17, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 31, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 10, 64)-net over F27, using
(44, 44+27, 504)-Net in Base 27 — Constructive
(44, 71, 504)-net in base 27, using
- net defined by OOA [i] based on OOA(2771, 504, S27, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(2771, 6553, S27, 27), using
- discarding factors based on OA(2771, 6563, S27, 27), using
- discarding parts of the base [i] based on linear OA(8153, 6563, F81, 27) (dual of [6563, 6510, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(8153, 6563, F81, 27) (dual of [6563, 6510, 28]-code), using
- discarding factors based on OA(2771, 6563, S27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(2771, 6553, S27, 27), using
(44, 44+27, 3302)-Net over F27 — Digital
Digital (44, 71, 3302)-net over F27, using
(44, 44+27, large)-Net in Base 27 — Upper bound on s
There is no (44, 71, large)-net in base 27, because
- 25 times m-reduction [i] would yield (44, 46, large)-net in base 27, but