Best Known (244−90, 244, s)-Nets in Base 3
(244−90, 244, 162)-Net over F3 — Constructive and digital
Digital (154, 244, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 122, 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
(244−90, 244, 281)-Net over F3 — Digital
Digital (154, 244, 281)-net over F3, using
(244−90, 244, 3361)-Net in Base 3 — Upper bound on s
There is no (154, 244, 3362)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 263 653399 329004 919958 082964 174363 244147 232977 770226 699770 053128 369315 707761 662594 642039 053080 693652 728657 879750 638669 > 3244 [i]