Best Known (48−25, 48, s)-Nets in Base 49
(48−25, 48, 344)-Net over F49 — Constructive and digital
Digital (23, 48, 344)-net over F49, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(48−25, 48, 548)-Net over F49 — Digital
Digital (23, 48, 548)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4948, 548, F49, 25) (dual of [548, 500, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4948, 800, F49, 25) (dual of [800, 752, 26]-code), using
(48−25, 48, 459250)-Net in Base 49 — Upper bound on s
There is no (23, 48, 459251)-net in base 49, because
- 1 times m-reduction [i] would yield (23, 47, 459251)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 27 493147 489854 537888 934717 419333 243639 882826 935363 925936 086184 789071 722726 481601 > 4947 [i]