Best Known (89, 89+79, s)-Nets in Base 3
(89, 89+79, 69)-Net over F3 — Constructive and digital
Digital (89, 168, 69)-net over F3, using
- 3 times m-reduction [i] based on digital (89, 171, 69)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (21, 62, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- digital (27, 109, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- digital (21, 62, 32)-net over F3, using
- (u, u+v)-construction [i] based on
(89, 89+79, 102)-Net over F3 — Digital
Digital (89, 168, 102)-net over F3, using
(89, 89+79, 812)-Net in Base 3 — Upper bound on s
There is no (89, 168, 813)-net in base 3, because
- 1 times m-reduction [i] would yield (89, 167, 813)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 49 393183 314904 679575 692986 739512 516122 961605 197080 398185 504157 529231 348687 695611 > 3167 [i]