Best Known (65, 65+18, s)-Nets in Base 3
(65, 65+18, 464)-Net over F3 — Constructive and digital
Digital (65, 83, 464)-net over F3, using
- 1 times m-reduction [i] based on digital (65, 84, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 21, 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, 21, 116)-net over F81, using
(65, 65+18, 933)-Net over F3 — Digital
Digital (65, 83, 933)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(383, 933, F3, 18) (dual of [933, 850, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(383, 1092, F3, 18) (dual of [1092, 1009, 19]-code), using
(65, 65+18, 52091)-Net in Base 3 — Upper bound on s
There is no (65, 83, 52092)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3991 020007 646664 377219 178428 415223 431033 > 383 [i]