Best Known (29, 29+96, s)-Nets in Base 16
(29, 29+96, 65)-Net over F16 — Constructive and digital
Digital (29, 125, 65)-net over F16, using
- t-expansion [i] based on digital (6, 125, 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, 29+96, 66)-Net in Base 16 — Constructive
(29, 125, 66)-net in base 16, using
- t-expansion [i] based on (25, 125, 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, 29+96, 161)-Net over F16 — Digital
Digital (29, 125, 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, 29+96, 1681)-Net in Base 16 — Upper bound on s
There is no (29, 125, 1682)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 3 351033 416442 887790 169068 984566 336177 080454 157160 206432 640460 738413 363129 144285 895083 971309 039559 331632 795131 072591 316292 722093 364000 086259 495996 355316 > 16125 [i]