Best Known (130−33, 130, s)-Nets in Base 2
(130−33, 130, 138)-Net over F2 — Constructive and digital
Digital (97, 130, 138)-net over F2, using
- 21 times duplication [i] based on digital (96, 129, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 43, 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, 43, 46)-net over F8, using
(130−33, 130, 190)-Net over F2 — Digital
Digital (97, 130, 190)-net over F2, using
(130−33, 130, 1794)-Net in Base 2 — Upper bound on s
There is no (97, 130, 1795)-net in base 2, because
- 1 times m-reduction [i] would yield (97, 129, 1795)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 682 763732 304805 798642 519347 717896 936208 > 2129 [i]