Best Known (100, 100+39, s)-Nets in Base 9
(100, 100+39, 780)-Net over F9 — Constructive and digital
Digital (100, 139, 780)-net over F9, using
- 1 times m-reduction [i] based on digital (100, 140, 780)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 28, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- digital (72, 112, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 56, 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
- trace code for nets [i] based on digital (16, 56, 370)-net over F81, using
- digital (8, 28, 40)-net over F9, using
- (u, u+v)-construction [i] based on
(100, 100+39, 6573)-Net over F9 — Digital
Digital (100, 139, 6573)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9139, 6573, F9, 39) (dual of [6573, 6434, 40]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9138, 6571, F9, 39) (dual of [6571, 6433, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(9137, 6562, F9, 39) (dual of [6562, 6425, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(9129, 6562, F9, 37) (dual of [6562, 6433, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(9138, 6572, F9, 38) (dual of [6572, 6434, 39]-code), using Gilbert–Varšamov bound and bm = 9138 > Vbs−1(k−1) = 304905 315385 322616 904672 978932 697780 044200 163653 553614 103323 164887 182737 445288 031434 195489 338453 263310 427800 833831 693261 861442 595097 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(9138, 6571, F9, 39) (dual of [6571, 6433, 40]-code), using
- construction X with Varšamov bound [i] based on
(100, 100+39, large)-Net in Base 9 — Upper bound on s
There is no (100, 139, large)-net in base 9, because
- 37 times m-reduction [i] would yield (100, 102, large)-net in base 9, but