Best Known (254−142, 254, s)-Nets in Base 2
(254−142, 254, 57)-Net over F2 — Constructive and digital
Digital (112, 254, 57)-net over F2, using
- t-expansion [i] based on digital (110, 254, 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
(254−142, 254, 72)-Net over F2 — Digital
Digital (112, 254, 72)-net over F2, using
- t-expansion [i] based on digital (110, 254, 72)-net over F2, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 110 and N(F) ≥ 72, using
- net from sequence [i] based on digital (110, 71)-sequence over F2, using
(254−142, 254, 232)-Net in Base 2 — Upper bound on s
There is no (112, 254, 233)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 29173 216854 981896 491706 744023 362779 768462 819310 634246 902938 045409 331206 995712 > 2254 [i]