Best Known (128−105, 128, s)-Nets in Base 2
(128−105, 128, 21)-Net over F2 — Constructive and digital
Digital (23, 128, 21)-net over F2, using
- t-expansion [i] based on digital (21, 128, 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
(128−105, 128, 22)-Net over F2 — Digital
Digital (23, 128, 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
(128−105, 128, 31)-Net in Base 2 — Upper bound on s
There is no (23, 128, 32)-net in base 2, because
- 7 times m-reduction [i] would yield (23, 121, 32)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2121, 32, S2, 4, 98), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 340 282366 920938 463463 374607 431768 211456 / 99 > 2121 [i]
- extracting embedded OOA [i] would yield OOA(2121, 32, S2, 4, 98), but