Best Known (245−122, 245, s)-Nets in Base 3
(245−122, 245, 78)-Net over F3 — Constructive and digital
Digital (123, 245, 78)-net over F3, using
- t-expansion [i] based on digital (121, 245, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
(245−122, 245, 121)-Net over F3 — Digital
Digital (123, 245, 121)-net over F3, using
(245−122, 245, 912)-Net in Base 3 — Upper bound on s
There is no (123, 245, 913)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 802 573317 705356 098283 817546 810652 028047 074919 015682 166943 949951 374096 526331 081885 959392 654363 110662 075595 095110 833459 > 3245 [i]