Best Known (35, 88, s)-Nets in Base 9
(35, 88, 81)-Net over F9 — Constructive and digital
Digital (35, 88, 81)-net over F9, using
- t-expansion [i] based on digital (32, 88, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(35, 88, 128)-Net over F9 — Digital
Digital (35, 88, 128)-net over F9, using
- t-expansion [i] based on digital (33, 88, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
(35, 88, 2041)-Net in Base 9 — Upper bound on s
There is no (35, 88, 2042)-net in base 9, because
- 1 times m-reduction [i] would yield (35, 87, 2042)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 105373 695433 898835 783874 484145 659286 716005 506178 837745 672341 590656 984770 527324 904929 > 987 [i]