Best Known (89, 126, s)-Nets in Base 3
(89, 126, 204)-Net over F3 — Constructive and digital
Digital (89, 126, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 42, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
(89, 126, 325)-Net over F3 — Digital
Digital (89, 126, 325)-net over F3, using
(89, 126, 7752)-Net in Base 3 — Upper bound on s
There is no (89, 126, 7753)-net in base 3, because
- 1 times m-reduction [i] would yield (89, 125, 7753)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 436780 950729 755888 057750 926176 331076 431429 076079 254802 503577 > 3125 [i]