Best Known (54−49, 54, s)-Nets in Base 32
(54−49, 54, 76)-Net over F32 — Constructive and digital
Digital (5, 54, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
(54−49, 54, 83)-Net over F32 — Digital
Digital (5, 54, 83)-net over F32, using
- net from sequence [i] based on digital (5, 82)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 83, using
(54−49, 54, 642)-Net in Base 32 — Upper bound on s
There is no (5, 54, 643)-net in base 32, because
- 9 times m-reduction [i] would yield (5, 45, 643)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 55 060154 278010 259113 428435 984399 934726 178167 489468 232883 386151 191712 > 3245 [i]