Best Known (33, 33+78, s)-Nets in Base 9
(33, 33+78, 81)-Net over F9 — Constructive and digital
Digital (33, 111, 81)-net over F9, using
- t-expansion [i] based on digital (32, 111, 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
(33, 33+78, 128)-Net over F9 — Digital
Digital (33, 111, 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
(33, 33+78, 976)-Net in Base 9 — Upper bound on s
There is no (33, 111, 977)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8373 970625 237201 312526 808901 434040 925524 231385 852609 930309 408121 970295 539758 957739 870704 330683 819730 349049 > 9111 [i]