Best Known (111−24, 111, s)-Nets in Base 3
(111−24, 111, 464)-Net over F3 — Constructive and digital
Digital (87, 111, 464)-net over F3, using
- t-expansion [i] based on digital (86, 111, 464)-net over F3, using
- 1 times m-reduction [i] based on digital (86, 112, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 28, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 28, 116)-net over F81, using
- 1 times m-reduction [i] based on digital (86, 112, 464)-net over F3, using
(111−24, 111, 1080)-Net over F3 — Digital
Digital (87, 111, 1080)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3111, 1080, F3, 24) (dual of [1080, 969, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3111, 1092, F3, 24) (dual of [1092, 981, 25]-code), using
(111−24, 111, 68490)-Net in Base 3 — Upper bound on s
There is no (87, 111, 68491)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 91306 139051 283437 463701 728599 767984 394020 713564 657353 > 3111 [i]