Best Known (21, 21+27, s)-Nets in Base 49
(21, 21+27, 344)-Net over F49 — Constructive and digital
Digital (21, 48, 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
(21, 21+27, 152354)-Net in Base 49 — Upper bound on s
There is no (21, 48, 152355)-net in base 49, because
- 1 times m-reduction [i] would yield (21, 47, 152355)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 27 493206 297465 535315 451291 543800 035069 343738 252915 528346 643484 097391 175229 405521 > 4947 [i]