Best Known (26, 36, s)-Nets in Base 3
(26, 36, 144)-Net over F3 — Constructive and digital
Digital (26, 36, 144)-net over F3, using
- trace code for nets [i] based on digital (2, 12, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
(26, 36, 224)-Net over F3 — Digital
Digital (26, 36, 224)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(336, 224, F3, 10) (dual of [224, 188, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(336, 365, F3, 10) (dual of [365, 329, 11]-code), using
(26, 36, 3544)-Net in Base 3 — Upper bound on s
There is no (26, 36, 3545)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 150246 087159 983139 > 336 [i]