Best Known (216−78, 216, s)-Nets in Base 3
(216−78, 216, 156)-Net over F3 — Constructive and digital
Digital (138, 216, 156)-net over F3, using
- 16 times m-reduction [i] based on digital (138, 232, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 116, 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, 116, 78)-net over F9, using
(216−78, 216, 268)-Net over F3 — Digital
Digital (138, 216, 268)-net over F3, using
(216−78, 216, 3341)-Net in Base 3 — Upper bound on s
There is no (138, 216, 3342)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 479678 664578 975795 256545 453875 218939 787130 504883 389544 128822 513507 908213 284867 263363 150544 825902 806201 > 3216 [i]