Best Known (38, 38+38, s)-Nets in Base 27
(38, 38+38, 182)-Net over F27 — Constructive and digital
Digital (38, 76, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 28, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 48, 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 (9, 28, 88)-net over F27, using
(38, 38+38, 370)-Net in Base 27 — Constructive
(38, 76, 370)-net in base 27, using
- 12 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, 38+38, 511)-Net over F27 — Digital
Digital (38, 76, 511)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2776, 511, F27, 38) (dual of [511, 435, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, 743, F27, 38) (dual of [743, 667, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- linear OA(2772, 729, F27, 38) (dual of [729, 657, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2762, 729, F27, 33) (dual of [729, 667, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(2776, 743, F27, 38) (dual of [743, 667, 39]-code), using
(38, 38+38, 162058)-Net in Base 27 — Upper bound on s
There is no (38, 76, 162059)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 6 076931 935623 678230 520794 810204 706096 885553 055505 740404 878836 623730 208624 044018 534188 810190 023144 055951 990595 > 2776 [i]