Best Known (72, 72+38, s)-Nets in Base 3
(72, 72+38, 148)-Net over F3 — Constructive and digital
Digital (72, 110, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 55, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
(72, 72+38, 175)-Net over F3 — Digital
Digital (72, 110, 175)-net over F3, using
(72, 72+38, 2274)-Net in Base 3 — Upper bound on s
There is no (72, 110, 2275)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 30459 845939 664192 352715 781349 746740 511742 660971 143691 > 3110 [i]