Best Known (111−21, 111, s)-Nets in Base 3
(111−21, 111, 640)-Net over F3 — Constructive and digital
Digital (90, 111, 640)-net over F3, using
- t-expansion [i] based on digital (89, 111, 640)-net over F3, using
- 1 times m-reduction [i] based on digital (89, 112, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 28, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 28, 160)-net over F81, using
- 1 times m-reduction [i] based on digital (89, 112, 640)-net over F3, using
(111−21, 111, 2276)-Net over F3 — Digital
Digital (90, 111, 2276)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3111, 2276, F3, 21) (dual of [2276, 2165, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3111, 3280, F3, 21) (dual of [3280, 3169, 22]-code), using
(111−21, 111, 401115)-Net in Base 3 — Upper bound on s
There is no (90, 111, 401116)-net in base 3, because
- 1 times m-reduction [i] would yield (90, 110, 401116)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 30432 640605 421340 850705 606569 038616 221459 215581 798217 > 3110 [i]