Best Known (194, 194+39, s)-Nets in Base 3
(194, 194+39, 1480)-Net over F3 — Constructive and digital
Digital (194, 233, 1480)-net over F3, using
- t-expansion [i] based on digital (193, 233, 1480)-net over F3, using
- 3 times m-reduction [i] based on digital (193, 236, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 59, 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, 59, 370)-net over F81, using
- 3 times m-reduction [i] based on digital (193, 236, 1480)-net over F3, using
(194, 194+39, 7152)-Net over F3 — Digital
Digital (194, 233, 7152)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3233, 7152, F3, 39) (dual of [7152, 6919, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(3233, 9840, F3, 39) (dual of [9840, 9607, 40]-code), using
(194, 194+39, 2655119)-Net in Base 3 — Upper bound on s
There is no (194, 233, 2655120)-net in base 3, because
- 1 times m-reduction [i] would yield (194, 232, 2655120)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 492 188790 356149 728503 359796 851649 093213 853615 667728 432887 699380 382007 260101 097568 096770 262610 442915 144151 641665 > 3232 [i]