Best Known (63−24, 63, s)-Nets in Base 27
(63−24, 63, 234)-Net over F27 — Constructive and digital
Digital (39, 63, 234)-net over F27, using
- 1 times m-reduction [i] based on digital (39, 64, 234)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 14, 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, 18, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (7, 32, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (6, 14, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(63−24, 63, 546)-Net in Base 27 — Constructive
(39, 63, 546)-net in base 27, using
- net defined by OOA [i] based on OOA(2763, 546, S27, 24, 24), using
- OA 12-folding and stacking [i] based on OA(2763, 6552, S27, 24), using
- discarding factors based on OA(2763, 6563, S27, 24), using
- discarding parts of the base [i] based on linear OA(8147, 6563, F81, 24) (dual of [6563, 6516, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- 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(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(8147, 6563, F81, 24) (dual of [6563, 6516, 25]-code), using
- discarding factors based on OA(2763, 6563, S27, 24), using
- OA 12-folding and stacking [i] based on OA(2763, 6552, S27, 24), using
(63−24, 63, 3033)-Net over F27 — Digital
Digital (39, 63, 3033)-net over F27, using
(63−24, 63, 6653458)-Net in Base 27 — Upper bound on s
There is no (39, 63, 6653459)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 499400 672373 770003 949894 610283 344695 729340 018146 881922 244397 879751 098542 739077 104171 611177 > 2763 [i]