Best Known (151, 151+80, s)-Nets in Base 3
(151, 151+80, 162)-Net over F3 — Constructive and digital
Digital (151, 231, 162)-net over F3, using
- 7 times m-reduction [i] based on digital (151, 238, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 119, 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
- trace code for nets [i] based on digital (32, 119, 81)-net over F9, using
(151, 151+80, 321)-Net over F3 — Digital
Digital (151, 231, 321)-net over F3, using
(151, 151+80, 4449)-Net in Base 3 — Upper bound on s
There is no (151, 231, 4450)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 164 783970 659870 515207 400943 897710 862079 450283 750264 096250 637659 537817 220686 775046 780294 985651 516234 003232 275857 > 3231 [i]