Best Known (144−116, 144, s)-Nets in Base 2
(144−116, 144, 21)-Net over F2 — Constructive and digital
Digital (28, 144, 21)-net over F2, using
- t-expansion [i] based on digital (21, 144, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(144−116, 144, 25)-Net over F2 — Digital
Digital (28, 144, 25)-net over F2, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
(144−116, 144, 37)-Net in Base 2 — Upper bound on s
There is no (28, 144, 38)-net in base 2, because
- 1 times m-reduction [i] would yield (28, 143, 38)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2143, 38, S2, 4, 115), but
- the LP bound with quadratic polynomials shows that M ≥ 386 081651 249561 413137 837122 595224 758572 285952 / 29 > 2143 [i]
- extracting embedded OOA [i] would yield OOA(2143, 38, S2, 4, 115), but