Best Known (89, 89+120, s)-Nets in Base 3
(89, 89+120, 64)-Net over F3 — Constructive and digital
Digital (89, 209, 64)-net over F3, using
- net from sequence [i] based on digital (89, 63)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- base reduction for sequences [i] based on digital (13, 63)-sequence over F9, using
(89, 89+120, 96)-Net over F3 — Digital
Digital (89, 209, 96)-net over F3, using
- net from sequence [i] based on digital (89, 95)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 89 and N(F) ≥ 96, using
(89, 89+120, 475)-Net in Base 3 — Upper bound on s
There is no (89, 209, 476)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5494 132735 404278 898955 485005 595256 733803 961050 467860 967341 838932 092468 754032 899428 348354 251066 999489 > 3209 [i]