Best Known (246−156, 246, s)-Nets in Base 2
(246−156, 246, 53)-Net over F2 — Constructive and digital
Digital (90, 246, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 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]
(246−156, 246, 57)-Net over F2 — Digital
Digital (90, 246, 57)-net over F2, using
- t-expansion [i] based on digital (83, 246, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(246−156, 246, 168)-Net in Base 2 — Upper bound on s
There is no (90, 246, 169)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 142 349004 649126 397271 754774 108380 864489 760359 620687 984736 420517 660971 704800 > 2246 [i]