Best Known (44, 44+26, s)-Nets in Base 27
(44, 44+26, 260)-Net over F27 — Constructive and digital
Digital (44, 70, 260)-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, 12, 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 (5, 31, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 10, 64)-net over F27, using
(44, 44+26, 505)-Net in Base 27 — Constructive
(44, 70, 505)-net in base 27, using
- net defined by OOA [i] based on OOA(2770, 505, S27, 26, 26), using
- OA 13-folding and stacking [i] based on OA(2770, 6565, S27, 26), using
- discarding factors based on OA(2770, 6566, S27, 26), using
- discarding parts of the base [i] based on linear OA(8152, 6566, F81, 26) (dual of [6566, 6514, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- 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(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(8152, 6566, F81, 26) (dual of [6566, 6514, 27]-code), using
- discarding factors based on OA(2770, 6566, S27, 26), using
- OA 13-folding and stacking [i] based on OA(2770, 6565, S27, 26), using
(44, 44+26, 3998)-Net over F27 — Digital
Digital (44, 70, 3998)-net over F27, using
(44, 44+26, large)-Net in Base 27 — Upper bound on s
There is no (44, 70, large)-net in base 27, because
- 24 times m-reduction [i] would yield (44, 46, large)-net in base 27, but