Best Known (259−159, 259, s)-Nets in Base 2
(259−159, 259, 55)-Net over F2 — Constructive and digital
Digital (100, 259, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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]
(259−159, 259, 65)-Net over F2 — Digital
Digital (100, 259, 65)-net over F2, using
- t-expansion [i] based on digital (95, 259, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(259−159, 259, 190)-Net in Base 2 — Upper bound on s
There is no (100, 259, 191)-net in base 2, because
- 1 times m-reduction [i] would yield (100, 258, 191)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 488639 289836 058922 670797 896338 983063 286312 898913 541366 166059 328295 195056 072468 > 2258 [i]