Best Known (260−144, 260, s)-Nets in Base 2
(260−144, 260, 57)-Net over F2 — Constructive and digital
Digital (116, 260, 57)-net over F2, using
- t-expansion [i] based on digital (110, 260, 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
(260−144, 260, 73)-Net over F2 — Digital
Digital (116, 260, 73)-net over F2, using
- t-expansion [i] based on digital (114, 260, 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
(260−144, 260, 243)-Net in Base 2 — Upper bound on s
There is no (116, 260, 244)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2 025468 023991 864026 804310 011810 965390 864363 603925 758318 667284 146214 707106 309378 > 2260 [i]