Best Known (107−59, 107, s)-Nets in Base 16
(107−59, 107, 243)-Net over F16 — Constructive and digital
Digital (48, 107, 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
(107−59, 107, 257)-Net in Base 16
(48, 107, 257)-net in base 16, using
- 1 times m-reduction [i] based on (48, 108, 257)-net in base 16, using
- base change [i] based on digital (12, 72, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 72, 257)-net over F64, using
(107−59, 107, 19585)-Net in Base 16 — Upper bound on s
There is no (48, 107, 19586)-net in base 16, because
- 1 times m-reduction [i] would yield (48, 106, 19586)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 43 328527 098475 828191 327358 770385 210076 105461 246029 160421 288145 533416 386377 706696 736787 196676 007926 938477 528772 867602 381153 303136 > 16106 [i]