Best Known (60−22, 60, s)-Nets in Base 27
(60−22, 60, 262)-Net over F27 — Constructive and digital
Digital (38, 60, 262)-net over F27, using
- 1 times m-reduction [i] based on digital (38, 61, 262)-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, 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, 3, 28)-net over F27 (see above)
- 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, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 11, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (1, 24, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- generalized (u, u+v)-construction [i] based on
(60−22, 60, 597)-Net in Base 27 — Constructive
(38, 60, 597)-net in base 27, using
- base change [i] based on digital (23, 45, 597)-net over F81, using
- net defined by OOA [i] based on linear OOA(8145, 597, F81, 22, 22) (dual of [(597, 22), 13089, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8145, 6567, F81, 22) (dual of [6567, 6522, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 6569, F81, 22) (dual of [6569, 6524, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8145, 6569, F81, 22) (dual of [6569, 6524, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8145, 6567, F81, 22) (dual of [6567, 6522, 23]-code), using
- net defined by OOA [i] based on linear OOA(8145, 597, F81, 22, 22) (dual of [(597, 22), 13089, 23]-NRT-code), using
(60−22, 60, 4114)-Net over F27 — Digital
Digital (38, 60, 4114)-net over F27, using
(60−22, 60, large)-Net in Base 27 — Upper bound on s
There is no (38, 60, large)-net in base 27, because
- 20 times m-reduction [i] would yield (38, 40, large)-net in base 27, but