Best Known (127, 127+79, s)-Nets in Base 2
(127, 127+79, 68)-Net over F2 — Constructive and digital
Digital (127, 206, 68)-net over F2, using
- 6 times m-reduction [i] based on digital (127, 212, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 106, 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, 106, 34)-net over F4, using
(127, 127+79, 70)-Net in Base 2 — Constructive
(127, 206, 70)-net in base 2, using
- trace code for nets [i] based on (24, 103, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-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 2 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]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(127, 127+79, 104)-Net over F2 — Digital
Digital (127, 206, 104)-net over F2, using
(127, 127+79, 533)-Net in Base 2 — Upper bound on s
There is no (127, 206, 534)-net in base 2, because
- 1 times m-reduction [i] would yield (127, 205, 534)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 54 944318 933831 449066 899042 704936 717043 069101 535339 298053 814848 > 2205 [i]