Best Known (253−143, 253, s)-Nets in Base 2
(253−143, 253, 57)-Net over F2 — Constructive and digital
Digital (110, 253, 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]
(253−143, 253, 72)-Net over F2 — Digital
Digital (110, 253, 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
(253−143, 253, 226)-Net in Base 2 — Upper bound on s
There is no (110, 253, 227)-net in base 2, because
- 1 times m-reduction [i] would yield (110, 252, 227)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7406 701838 562964 512044 732004 509248 792965 719962 509095 939865 836143 659252 375408 > 2252 [i]