Best Known (29, 127, s)-Nets in Base 16
(29, 127, 65)-Net over F16 — Constructive and digital
Digital (29, 127, 65)-net over F16, using
- t-expansion [i] based on digital (6, 127, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(29, 127, 66)-Net in Base 16 — Constructive
(29, 127, 66)-net in base 16, using
- t-expansion [i] based on (25, 127, 66)-net in base 16, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
(29, 127, 161)-Net over F16 — Digital
Digital (29, 127, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
(29, 127, 1655)-Net in Base 16 — Upper bound on s
There is no (29, 127, 1656)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 840 402467 802173 355213 136424 196343 609980 060878 256722 061628 279386 542988 772666 143360 181192 796931 881495 489559 160106 162582 923007 637438 312074 297606 792138 973511 > 16127 [i]