Best Known (194−71, 194, s)-Nets in Base 2
(194−71, 194, 68)-Net over F2 — Constructive and digital
Digital (123, 194, 68)-net over F2, using
- 10 times m-reduction [i] based on digital (123, 204, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 102, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- trace code for nets [i] based on digital (21, 102, 34)-net over F4, using
(194−71, 194, 72)-Net in Base 2 — Constructive
(123, 194, 72)-net in base 2, using
- trace code for nets [i] based on (26, 97, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
(194−71, 194, 110)-Net over F2 — Digital
Digital (123, 194, 110)-net over F2, using
- trace code for nets [i] based on digital (26, 97, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(194−71, 194, 585)-Net in Base 2 — Upper bound on s
There is no (123, 194, 586)-net in base 2, because
- 1 times m-reduction [i] would yield (123, 193, 586)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 12885 010381 868835 692515 436754 542731 662222 112329 722906 780000 > 2193 [i]