Best Known (114−23, 114, s)-Nets in Base 9
(114−23, 114, 5388)-Net over F9 — Constructive and digital
Digital (91, 114, 5388)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (78, 101, 5368)-net over F9, using
- net defined by OOA [i] based on linear OOA(9101, 5368, F9, 23, 23) (dual of [(5368, 23), 123363, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on 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]
- OOA 11-folding and stacking with additional row [i] based on linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using
- net defined by OOA [i] based on linear OOA(9101, 5368, F9, 23, 23) (dual of [(5368, 23), 123363, 24]-NRT-code), using
- digital (2, 13, 20)-net over F9, using
(114−23, 114, 99660)-Net over F9 — Digital
Digital (91, 114, 99660)-net over F9, using
(114−23, 114, large)-Net in Base 9 — Upper bound on s
There is no (91, 114, large)-net in base 9, because
- 21 times m-reduction [i] would yield (91, 93, large)-net in base 9, but