Best Known (51, 116, s)-Nets in Base 9
(51, 116, 98)-Net over F9 — Constructive and digital
Digital (51, 116, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 38, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (13, 78, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (6, 38, 34)-net over F9, using
(51, 116, 182)-Net over F9 — Digital
Digital (51, 116, 182)-net over F9, using
- t-expansion [i] based on digital (50, 116, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(51, 116, 4276)-Net in Base 9 — Upper bound on s
There is no (51, 116, 4277)-net in base 9, because
- 1 times m-reduction [i] would yield (51, 115, 4277)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 54 739081 190665 441864 356133 451919 492697 837107 195801 482556 540565 948132 061698 518466 740292 142240 805443 416015 771905 > 9115 [i]