Best Known (118, 118+54, s)-Nets in Base 3
(118, 118+54, 162)-Net over F3 — Constructive and digital
Digital (118, 172, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 86, 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
(118, 118+54, 337)-Net over F3 — Digital
Digital (118, 172, 337)-net over F3, using
(118, 118+54, 5955)-Net in Base 3 — Upper bound on s
There is no (118, 172, 5956)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11656 394579 410160 901944 402619 351153 815145 361486 789302 017148 732442 955537 532906 582641 > 3172 [i]