Best Known (99, 99+40, s)-Nets in Base 3
(99, 99+40, 228)-Net over F3 — Constructive and digital
Digital (99, 139, 228)-net over F3, using
- 31 times duplication [i] based on digital (98, 138, 228)-net over F3, using
- trace code for nets [i] based on digital (6, 46, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- trace code for nets [i] based on digital (6, 46, 76)-net over F27, using
(99, 99+40, 376)-Net over F3 — Digital
Digital (99, 139, 376)-net over F3, using
(99, 99+40, 8575)-Net in Base 3 — Upper bound on s
There is no (99, 139, 8576)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 088716 538616 810131 694998 113225 592194 887115 696595 944767 420184 867841 > 3139 [i]