Best Known (123, 123+46, s)-Nets in Base 2
(123, 123+46, 138)-Net over F2 — Constructive and digital
Digital (123, 169, 138)-net over F2, using
- 21 times duplication [i] based on digital (122, 168, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 56, 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, 56, 46)-net over F8, using
(123, 123+46, 196)-Net over F2 — Digital
Digital (123, 169, 196)-net over F2, using
(123, 123+46, 1502)-Net in Base 2 — Upper bound on s
There is no (123, 169, 1503)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 756 484223 434461 694471 969429 264690 624170 500286 622598 > 2169 [i]