Best Known (107−59, 107, s)-Nets in Base 9
(107−59, 107, 98)-Net over F9 — Constructive and digital
Digital (48, 107, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 35, 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, 72, 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, 35, 34)-net over F9, using
(107−59, 107, 163)-Net over F9 — Digital
Digital (48, 107, 163)-net over F9, using
- net from sequence [i] based on digital (48, 162)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 48 and N(F) ≥ 163, using
(107−59, 107, 4469)-Net in Base 9 — Upper bound on s
There is no (48, 107, 4470)-net in base 9, because
- 1 times m-reduction [i] would yield (48, 106, 4470)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 141740 350071 589946 596874 476305 540380 948618 612866 560667 361286 935525 071522 893090 018373 927000 149075 397233 > 9106 [i]