Best Known (106−83, 106, s)-Nets in Base 2
(106−83, 106, 21)-Net over F2 — Constructive and digital
Digital (23, 106, 21)-net over F2, using
- t-expansion [i] based on digital (21, 106, 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
(106−83, 106, 22)-Net over F2 — Digital
Digital (23, 106, 22)-net over F2, using
- net from sequence [i] based on digital (23, 21)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 23 and N(F) ≥ 22, using
(106−83, 106, 33)-Net in Base 2 — Upper bound on s
There is no (23, 106, 34)-net in base 2, because
- 12 times m-reduction [i] would yield (23, 94, 34)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(294, 34, S2, 3, 71), but
- the LP bound with quadratic polynomials shows that M ≥ 188166 885971 377801 784666 882048 / 9 > 294 [i]
- extracting embedded OOA [i] would yield OOA(294, 34, S2, 3, 71), but