Best Known (72, 72+56, s)-Nets in Base 3
(72, 72+56, 80)-Net over F3 — Constructive and digital
Digital (72, 128, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 64, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(72, 72+56, 100)-Net over F3 — Digital
Digital (72, 128, 100)-net over F3, using
(72, 72+56, 830)-Net in Base 3 — Upper bound on s
There is no (72, 128, 831)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 12 142275 025307 033315 939458 065484 971514 769984 822743 173894 581193 > 3128 [i]