Best Known (95, 132, s)-Nets in Base 9
(95, 132, 780)-Net over F9 — Constructive and digital
Digital (95, 132, 780)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (8, 26, 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 (69, 106, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 53, 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, 53, 370)-net over F81, using
- digital (8, 26, 40)-net over F9, using
(95, 132, 6462)-Net over F9 — Digital
Digital (95, 132, 6462)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9132, 6462, F9, 37) (dual of [6462, 6330, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(9132, 6572, F9, 37) (dual of [6572, 6440, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- 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(9121, 6562, F9, 33) (dual of [6562, 6441, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(93, 10, F9, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,9) or 10-cap in PG(2,9)), using
- extended Reed–Solomon code RSe(7,9) [i]
- oval in PG(2, 9) [i]
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9132, 6572, F9, 37) (dual of [6572, 6440, 38]-code), using
(95, 132, 8313893)-Net in Base 9 — Upper bound on s
There is no (95, 132, 8313894)-net in base 9, because
- 1 times m-reduction [i] would yield (95, 131, 8313894)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 101337 351268 110180 996721 040177 369433 899442 133790 845975 623866 036791 821892 056468 681774 466169 924328 098529 893533 009771 193121 410209 > 9131 [i]