Best Known (118−17, 118, s)-Nets in Base 9
(118−17, 118, 597901)-Net over F9 — Constructive and digital
Digital (101, 118, 597901)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- digital (89, 106, 597871)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 597871, F9, 17, 17) (dual of [(597871, 17), 10163701, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
- net defined by OOA [i] based on linear OOA(9106, 597871, F9, 17, 17) (dual of [(597871, 17), 10163701, 18]-NRT-code), using
- digital (4, 12, 30)-net over F9, using
(118−17, 118, large)-Net over F9 — Digital
Digital (101, 118, large)-net over F9, using
(118−17, 118, large)-Net in Base 9 — Upper bound on s
There is no (101, 118, large)-net in base 9, because
- 15 times m-reduction [i] would yield (101, 103, large)-net in base 9, but