Best Known (158−28, 158, s)-Nets in Base 3
(158−28, 158, 700)-Net over F3 — Constructive and digital
Digital (130, 158, 700)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 18, 12)-net over F3, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- digital (112, 140, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 35, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 35, 172)-net over F81, using
- digital (4, 18, 12)-net over F3, using
(158−28, 158, 3987)-Net over F3 — Digital
Digital (130, 158, 3987)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3158, 3987, F3, 28) (dual of [3987, 3829, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3158, 6606, F3, 28) (dual of [6606, 6448, 29]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3156, 6604, F3, 28) (dual of [6604, 6448, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3156, 6604, F3, 28) (dual of [6604, 6448, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3158, 6606, F3, 28) (dual of [6606, 6448, 29]-code), using
(158−28, 158, 732949)-Net in Base 3 — Upper bound on s
There is no (130, 158, 732950)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2427 529196 003416 651914 633019 121900 168257 568157 056558 178256 267225 623206 287941 > 3158 [i]