Best Known (99, 99+30, s)-Nets in Base 9
(99, 99+30, 972)-Net over F9 — Constructive and digital
Digital (99, 129, 972)-net over F9, using
- 91 times duplication [i] based on digital (98, 128, 972)-net over F9, using
- t-expansion [i] based on digital (97, 128, 972)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (19, 34, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 17, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 17, 116)-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 (19, 34, 232)-net over F9, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (97, 128, 972)-net over F9, using
(99, 99+30, 1312)-Net in Base 9 — Constructive
(99, 129, 1312)-net in base 9, using
- base change [i] based on digital (56, 86, 1312)-net over F27, using
- 271 times duplication [i] based on digital (55, 85, 1312)-net over F27, using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(2785, 19683, F27, 30) (dual of [19683, 19598, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2785, 19680, F27, 30) (dual of [19680, 19595, 31]-code), using
- net defined by OOA [i] based on linear OOA(2785, 1312, F27, 30, 30) (dual of [(1312, 30), 39275, 31]-NRT-code), using
- 271 times duplication [i] based on digital (55, 85, 1312)-net over F27, using
(99, 99+30, 25645)-Net over F9 — Digital
Digital (99, 129, 25645)-net over F9, using
(99, 99+30, large)-Net in Base 9 — Upper bound on s
There is no (99, 129, large)-net in base 9, because
- 28 times m-reduction [i] would yield (99, 101, large)-net in base 9, but