Best Known (258−150, 258, s)-Nets in Base 2
(258−150, 258, 56)-Net over F2 — Constructive and digital
Digital (108, 258, 56)-net over F2, using
- t-expansion [i] based on digital (105, 258, 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
(258−150, 258, 65)-Net over F2 — Digital
Digital (108, 258, 65)-net over F2, using
- t-expansion [i] based on digital (95, 258, 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
(258−150, 258, 215)-Net in Base 2 — Upper bound on s
There is no (108, 258, 216)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 531479 660299 903696 174495 045975 196447 327113 336536 616810 482004 928168 284109 076278 > 2258 [i]