Best Known (38, 72, s)-Nets in Base 27
(38, 72, 190)-Net over F27 — Constructive and digital
Digital (38, 72, 190)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 27, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (11, 45, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (10, 27, 94)-net over F27, using
(38, 72, 370)-Net in Base 27 — Constructive
(38, 72, 370)-net in base 27, using
- 16 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 66, 370)-net over F81, using
(38, 72, 723)-Net over F27 — Digital
Digital (38, 72, 723)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2772, 723, F27, 34) (dual of [723, 651, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2772, 752, F27, 34) (dual of [752, 680, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- linear OA(2764, 729, F27, 34) (dual of [729, 665, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2749, 729, F27, 25) (dual of [729, 680, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(278, 23, F27, 8) (dual of [23, 15, 9]-code or 23-arc in PG(7,27)), using
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), using
- Reed–Solomon code RS(19,27) [i]
- discarding factors / shortening the dual code based on linear OA(278, 27, F27, 8) (dual of [27, 19, 9]-code or 27-arc in PG(7,27)), using
- construction X applied to Ce(33) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2772, 752, F27, 34) (dual of [752, 680, 35]-code), using
(38, 72, 318571)-Net in Base 27 — Upper bound on s
There is no (38, 72, 318572)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 11 434263 246503 520182 392509 114025 144203 500450 698893 149862 693492 558841 632601 870018 026421 765299 344216 669433 > 2772 [i]