Best Known (32, 32+49, s)-Nets in Base 9
(32, 32+49, 81)-Net over F9 — Constructive and digital
Digital (32, 81, 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
(32, 32+49, 120)-Net over F9 — Digital
Digital (32, 81, 120)-net over F9, using
- t-expansion [i] based on digital (31, 81, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
(32, 32+49, 1843)-Net in Base 9 — Upper bound on s
There is no (32, 81, 1844)-net in base 9, because
- 1 times m-reduction [i] would yield (32, 80, 1844)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21936 469650 934901 986427 562128 646445 524634 849180 734821 486135 677218 566270 316801 > 980 [i]