Best Known (25, 25+29, s)-Nets in Base 49
(25, 25+29, 344)-Net over F49 — Constructive and digital
Digital (25, 54, 344)-net over F49, using
- t-expansion [i] based on digital (21, 54, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(25, 25+29, 442)-Net over F49 — Digital
Digital (25, 54, 442)-net over F49, using
(25, 25+29, 315359)-Net in Base 49 — Upper bound on s
There is no (25, 54, 315360)-net in base 49, because
- 1 times m-reduction [i] would yield (25, 53, 315360)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 380533 073815 894894 526059 415968 362377 296039 709265 283706 507516 936395 747226 016701 834811 177985 > 4953 [i]