Best Known (114, 114+100, s)-Nets in Base 2
(114, 114+100, 57)-Net over F2 — Constructive and digital
Digital (114, 214, 57)-net over F2, using
- t-expansion [i] based on digital (110, 214, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(114, 114+100, 73)-Net over F2 — Digital
Digital (114, 214, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
(114, 114+100, 245)-Net in Base 2 — Upper bound on s
There is no (114, 214, 246)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2214, 246, S2, 100), but
- the linear programming bound shows that M ≥ 4 269161 474636 638112 765111 173059 732556 431789 093598 144733 527718 890183 852032 / 155 465527 > 2214 [i]