Best Known (113−65, 113, s)-Nets in Base 16
(113−65, 113, 243)-Net over F16 — Constructive and digital
Digital (48, 113, 243)-net over F16, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
(113−65, 113, 13952)-Net in Base 16 — Upper bound on s
There is no (48, 113, 13953)-net in base 16, because
- 1 times m-reduction [i] would yield (48, 112, 13953)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 727 206953 083789 710275 656968 824909 181669 951562 908495 490975 241297 697184 708556 476932 932608 195119 866384 981770 129239 523578 512038 525718 583916 > 16112 [i]