Best Known (142, 142+80, s)-Nets in Base 3
(142, 142+80, 156)-Net over F3 — Constructive and digital
Digital (142, 222, 156)-net over F3, using
- 18 times m-reduction [i] based on digital (142, 240, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 120, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- trace code for nets [i] based on digital (22, 120, 78)-net over F9, using
(142, 142+80, 276)-Net over F3 — Digital
Digital (142, 222, 276)-net over F3, using
(142, 142+80, 3466)-Net in Base 3 — Upper bound on s
There is no (142, 222, 3467)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 8386 749512 677639 746975 836128 517686 509119 117302 897898 599716 074744 659731 548110 710787 774736 592280 035387 877425 > 3222 [i]