Best Known (246−155, 246, s)-Nets in Base 2
(246−155, 246, 53)-Net over F2 — Constructive and digital
Digital (91, 246, 53)-net over F2, using
- t-expansion [i] based on 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]
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
(246−155, 246, 57)-Net over F2 — Digital
Digital (91, 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
(246−155, 246, 171)-Net in Base 2 — Upper bound on s
There is no (91, 246, 172)-net in base 2, because
- 1 times m-reduction [i] would yield (91, 245, 172)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 75 434648 015255 919165 394612 874918 294522 654867 853754 689183 890085 192405 776320 > 2245 [i]