Best Known (180, 180+52, s)-Nets in Base 2
(180, 180+52, 260)-Net over F2 — Constructive and digital
Digital (180, 232, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 58, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(180, 180+52, 423)-Net over F2 — Digital
Digital (180, 232, 423)-net over F2, using
(180, 180+52, 5083)-Net in Base 2 — Upper bound on s
There is no (180, 232, 5084)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6928 218796 284204 892879 033355 601691 700131 417550 355153 863447 341235 831375 > 2232 [i]