Best Known (21, 39, s)-Nets in Base 27
(21, 39, 152)-Net over F27 — Constructive and digital
Digital (21, 39, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 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, 24, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 15, 76)-net over F27, using
(21, 39, 200)-Net in Base 27 — Constructive
(21, 39, 200)-net in base 27, using
- 1 times m-reduction [i] based on (21, 40, 200)-net in base 27, using
- base change [i] based on digital (11, 30, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (1, 20, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 10, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (11, 30, 200)-net over F81, using
(21, 39, 649)-Net over F27 — Digital
Digital (21, 39, 649)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2739, 649, F27, 18) (dual of [649, 610, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2739, 743, F27, 18) (dual of [743, 704, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(2735, 729, F27, 18) (dual of [729, 694, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2725, 729, F27, 13) (dual of [729, 704, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(17) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2739, 743, F27, 18) (dual of [743, 704, 19]-code), using
(21, 39, 254300)-Net in Base 27 — Upper bound on s
There is no (21, 39, 254301)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 66 557424 918932 008474 368499 570272 431793 325405 584208 515347 > 2739 [i]