Best Known (39, 39+36, s)-Nets in Base 27
(39, 39+36, 190)-Net over F27 — Constructive and digital
Digital (39, 75, 190)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 28, 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, 47, 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, 28, 94)-net over F27, using
(39, 39+36, 370)-Net in Base 27 — Constructive
(39, 75, 370)-net in base 27, using
- 17 times m-reduction [i] based on (39, 92, 370)-net in base 27, using
- base change [i] based on digital (16, 69, 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, 69, 370)-net over F81, using
(39, 39+36, 663)-Net over F27 — Digital
Digital (39, 75, 663)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2775, 663, F27, 36) (dual of [663, 588, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2775, 751, F27, 36) (dual of [751, 676, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- linear OA(2768, 729, F27, 36) (dual of [729, 661, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2753, 729, F27, 28) (dual of [729, 676, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(277, 22, F27, 7) (dual of [22, 15, 8]-code or 22-arc in PG(6,27)), using
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- Reed–Solomon code RS(20,27) [i]
- discarding factors / shortening the dual code based on linear OA(277, 27, F27, 7) (dual of [27, 20, 8]-code or 27-arc in PG(6,27)), using
- construction X applied to Ce(35) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2775, 751, F27, 36) (dual of [751, 676, 37]-code), using
(39, 39+36, 267397)-Net in Base 27 — Upper bound on s
There is no (39, 75, 267398)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 225058 155028 260866 962344 627252 957025 071751 655664 157715 859692 491873 541529 130435 660967 318547 261149 247590 498253 > 2775 [i]