Best Known (26, 26+16, s)-Nets in Base 27
(26, 26+16, 224)-Net over F27 — Constructive and digital
Digital (26, 42, 224)-net over F27, using
- 1 times m-reduction [i] based on digital (26, 43, 224)-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, 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, 8, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 17, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- generalized (u, u+v)-construction [i] based on
(26, 26+16, 820)-Net in Base 27 — Constructive
(26, 42, 820)-net in base 27, using
- net defined by OOA [i] based on OOA(2742, 820, S27, 16, 16), using
- OA 8-folding and stacking [i] based on OA(2742, 6560, S27, 16), using
- discarding factors based on OA(2742, 6563, S27, 16), using
- discarding parts of the base [i] based on linear OA(8131, 6563, F81, 16) (dual of [6563, 6532, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(8129, 6561, F81, 15) (dual of [6561, 6532, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(8131, 6563, F81, 16) (dual of [6563, 6532, 17]-code), using
- discarding factors based on OA(2742, 6563, S27, 16), using
- OA 8-folding and stacking [i] based on OA(2742, 6560, S27, 16), using
(26, 26+16, 2523)-Net over F27 — Digital
Digital (26, 42, 2523)-net over F27, using
(26, 26+16, 4735612)-Net in Base 27 — Upper bound on s
There is no (26, 42, 4735613)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 310022 294354 348816 045499 486864 385206 038479 628560 275595 839137 > 2742 [i]