Best Known (233−130, 233, s)-Nets in Base 2
(233−130, 233, 55)-Net over F2 — Constructive and digital
Digital (103, 233, 55)-net over F2, using
- t-expansion [i] based on digital (100, 233, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(233−130, 233, 65)-Net over F2 — Digital
Digital (103, 233, 65)-net over F2, using
- t-expansion [i] based on digital (95, 233, 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
(233−130, 233, 215)-Net in Base 2 — Upper bound on s
There is no (103, 233, 216)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14796 036364 895567 201200 602973 739553 895421 711530 866239 291454 322895 604827 > 2233 [i]