Best Known (106, 106+154, s)-Nets in Base 2
(106, 106+154, 56)-Net over F2 — Constructive and digital
Digital (106, 260, 56)-net over F2, using
- t-expansion [i] based on digital (105, 260, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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]
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
(106, 106+154, 65)-Net over F2 — Digital
Digital (106, 260, 65)-net over F2, using
- t-expansion [i] based on digital (95, 260, 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
(106, 106+154, 207)-Net in Base 2 — Upper bound on s
There is no (106, 260, 208)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 972892 486302 511347 731512 585827 885979 417465 770689 579256 360333 474591 350463 406569 > 2260 [i]