Best Known (41−9, 41, s)-Nets in Base 3
(41−9, 41, 400)-Net over F3 — Constructive and digital
Digital (32, 41, 400)-net over F3, using
- 31 times duplication [i] based on digital (31, 40, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 10, 100)-net over F81, using
(41−9, 41, 894)-Net over F3 — Digital
Digital (32, 41, 894)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(341, 894, F3, 9) (dual of [894, 853, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(341, 1092, F3, 9) (dual of [1092, 1051, 10]-code), using
(41−9, 41, 65344)-Net in Base 3 — Upper bound on s
There is no (32, 41, 65345)-net in base 3, because
- 1 times m-reduction [i] would yield (32, 40, 65345)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 12 157694 664356 231761 > 340 [i]