Best Known (253−52, 253, s)-Nets in Base 2
(253−52, 253, 260)-Net over F2 — Constructive and digital
Digital (201, 253, 260)-net over F2, using
- 7 times m-reduction [i] based on digital (201, 260, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 65, 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
- trace code for nets [i] based on digital (6, 65, 65)-net over F16, using
(253−52, 253, 581)-Net over F2 — Digital
Digital (201, 253, 581)-net over F2, using
(253−52, 253, 8926)-Net in Base 2 — Upper bound on s
There is no (201, 253, 8927)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14495 170922 881543 735023 456243 129717 467224 674228 144940 843106 718551 918363 333917 > 2253 [i]