Best Known (72−24, 72, s)-Nets in Base 3
(72−24, 72, 84)-Net over F3 — Constructive and digital
Digital (48, 72, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 24, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
(72−24, 72, 141)-Net over F3 — Digital
Digital (48, 72, 141)-net over F3, using
(72−24, 72, 1916)-Net in Base 3 — Upper bound on s
There is no (48, 72, 1917)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 22624 616491 552069 902942 545751 519217 > 372 [i]