Best Known (99, 123, s)-Nets in Base 9
(99, 123, 4953)-Net over F9 — Constructive and digital
Digital (99, 123, 4953)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (82, 106, 4921)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 4921, F9, 24, 24) (dual of [(4921, 24), 117998, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9106, 59052, F9, 24) (dual of [59052, 58946, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 59054, F9, 24) (dual of [59054, 58948, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 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
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9106, 59054, F9, 24) (dual of [59054, 58948, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9106, 59052, F9, 24) (dual of [59052, 58946, 25]-code), using
- net defined by OOA [i] based on linear OOA(9106, 4921, F9, 24, 24) (dual of [(4921, 24), 117998, 25]-NRT-code), using
- digital (5, 17, 32)-net over F9, using
(99, 123, 149459)-Net over F9 — Digital
Digital (99, 123, 149459)-net over F9, using
(99, 123, large)-Net in Base 9 — Upper bound on s
There is no (99, 123, large)-net in base 9, because
- 22 times m-reduction [i] would yield (99, 101, large)-net in base 9, but