Best Known (132−31, 132, s)-Nets in Base 9
(132−31, 132, 1040)-Net over F9 — Constructive and digital
Digital (101, 132, 1040)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (23, 38, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 19, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 19, 150)-net over F81, using
- digital (63, 94, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 47, 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, 47, 370)-net over F81, using
- digital (23, 38, 300)-net over F9, using
(132−31, 132, 1312)-Net in Base 9 — Constructive
(101, 132, 1312)-net in base 9, using
- base change [i] based on digital (57, 88, 1312)-net over F27, using
- net defined by OOA [i] based on linear OOA(2788, 1312, F27, 31, 31) (dual of [(1312, 31), 40584, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2788, 19681, F27, 31) (dual of [19681, 19593, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2788, 19683, F27, 31) (dual of [19683, 19595, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(2788, 19683, F27, 31) (dual of [19683, 19595, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(2788, 19681, F27, 31) (dual of [19681, 19593, 32]-code), using
- net defined by OOA [i] based on linear OOA(2788, 1312, F27, 31, 31) (dual of [(1312, 31), 40584, 32]-NRT-code), using
(132−31, 132, 23803)-Net over F9 — Digital
Digital (101, 132, 23803)-net over F9, using
(132−31, 132, large)-Net in Base 9 — Upper bound on s
There is no (101, 132, large)-net in base 9, because
- 29 times m-reduction [i] would yield (101, 103, large)-net in base 9, but