Best Known (99, 99+21, s)-Nets in Base 9
(99, 99+21, 53160)-Net over F9 — Constructive and digital
Digital (99, 120, 53160)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (88, 109, 53144)-net over F9, using
- net defined by OOA [i] based on linear OOA(9109, 53144, F9, 21, 21) (dual of [(53144, 21), 1115915, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using
- net defined by OOA [i] based on linear OOA(9109, 53144, F9, 21, 21) (dual of [(53144, 21), 1115915, 22]-NRT-code), using
- digital (1, 11, 16)-net over F9, using
(99, 99+21, 551670)-Net over F9 — Digital
Digital (99, 120, 551670)-net over F9, using
(99, 99+21, large)-Net in Base 9 — Upper bound on s
There is no (99, 120, large)-net in base 9, because
- 19 times m-reduction [i] would yield (99, 101, large)-net in base 9, but