Best Known (219−102, 219, s)-Nets in Base 2
(219−102, 219, 57)-Net over F2 — Constructive and digital
Digital (117, 219, 57)-net over F2, using
- t-expansion [i] based on digital (110, 219, 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
(219−102, 219, 73)-Net over F2 — Digital
Digital (117, 219, 73)-net over F2, using
- t-expansion [i] based on digital (114, 219, 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
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
(219−102, 219, 254)-Net in Base 2 — Upper bound on s
There is no (117, 219, 255)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2219, 255, S2, 102), but
- the linear programming bound shows that M ≥ 4 315546 483021 279649 407406 332607 712947 119706 218538 384469 353739 197136 290283 782144 / 3 966731 656641 > 2219 [i]