Best Known (164, 164+33, s)-Nets in Base 3
(164, 164+33, 1480)-Net over F3 — Constructive and digital
Digital (164, 197, 1480)-net over F3, using
- 31 times duplication [i] based on digital (163, 196, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 49, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 49, 370)-net over F81, using
(164, 164+33, 6422)-Net over F3 — Digital
Digital (164, 197, 6422)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3197, 6422, F3, 33) (dual of [6422, 6225, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 9840, F3, 33) (dual of [9840, 9643, 34]-code), using
(164, 164+33, 2378161)-Net in Base 3 — Upper bound on s
There is no (164, 197, 2378162)-net in base 3, because
- 1 times m-reduction [i] would yield (164, 196, 2378162)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3279 205181 152644 749460 752316 191517 451201 655481 811224 762400 808937 190897 926370 713256 359484 025505 > 3196 [i]