Best Known (111−71, 111, s)-Nets in Base 16
(111−71, 111, 225)-Net over F16 — Constructive and digital
Digital (40, 111, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
(111−71, 111, 5624)-Net in Base 16 — Upper bound on s
There is no (40, 111, 5625)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 110, 5625)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 853381 362973 026396 784999 811690 373924 033072 575300 766009 190828 395236 793842 220574 544287 616391 708330 281739 737872 098214 322953 516887 484376 > 16110 [i]