Best Known (34, 34+15, s)-Nets in Base 3
(34, 34+15, 114)-Net over F3 — Constructive and digital
Digital (34, 49, 114)-net over F3, using
- 31 times duplication [i] based on digital (33, 48, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 16, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 16, 38)-net over F27, using
(34, 34+15, 154)-Net over F3 — Digital
Digital (34, 49, 154)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(349, 154, F3, 15) (dual of [154, 105, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(349, 161, F3, 15) (dual of [161, 112, 16]-code), using
- 1 times truncation [i] based on linear OA(350, 162, F3, 16) (dual of [162, 112, 17]-code), using
- a “Gra†code from Grassl’s database [i]
- 1 times truncation [i] based on linear OA(350, 162, F3, 16) (dual of [162, 112, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(349, 161, F3, 15) (dual of [161, 112, 16]-code), using
(34, 34+15, 3152)-Net in Base 3 — Upper bound on s
There is no (34, 49, 3153)-net in base 3, because
- 1 times m-reduction [i] would yield (34, 48, 3153)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 79818 314107 522258 793931 > 348 [i]