Best Known (81, 81+25, s)-Nets in Base 2
(81, 81+25, 138)-Net over F2 — Constructive and digital
Digital (81, 106, 138)-net over F2, using
- 21 times duplication [i] based on digital (80, 105, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 35, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 35, 46)-net over F8, using
(81, 81+25, 198)-Net over F2 — Digital
Digital (81, 106, 198)-net over F2, using
(81, 81+25, 2259)-Net in Base 2 — Upper bound on s
There is no (81, 106, 2260)-net in base 2, because
- 1 times m-reduction [i] would yield (81, 105, 2260)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 40 646731 235026 943020 434186 039908 > 2105 [i]