Best Known (141−61, 141, s)-Nets in Base 2
(141−61, 141, 51)-Net over F2 — Constructive and digital
Digital (80, 141, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 2 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(141−61, 141, 58)-Net over F2 — Digital
Digital (80, 141, 58)-net over F2, using
(141−61, 141, 264)-Net in Base 2 — Upper bound on s
There is no (80, 141, 265)-net in base 2, because
- 1 times m-reduction [i] would yield (80, 140, 265)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 515874 866857 954577 865557 320063 003000 531328 > 2140 [i]