Best Known (128−114, 128, s)-Nets in Base 2
(128−114, 128, 15)-Net over F2 — Constructive and digital
Digital (14, 128, 15)-net over F2, using
- t-expansion [i] based on digital (13, 128, 15)-net over F2, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 13 and N(F) ≥ 15, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
(128−114, 128, 21)-Net in Base 2 — Upper bound on s
There is no (14, 128, 22)-net in base 2, because
- 48 times m-reduction [i] would yield (14, 80, 22)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(280, 22, S2, 4, 66), but
- the LP bound with quadratic polynomials shows that M ≥ 83 718113 008313 070348 402688 / 67 > 280 [i]
- extracting embedded OOA [i] would yield OOA(280, 22, S2, 4, 66), but