Best Known (77−53, 77, s)-Nets in Base 128
(77−53, 77, 288)-Net over F128 — Constructive and digital
Digital (24, 77, 288)-net over F128, using
- t-expansion [i] based on digital (9, 77, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(77−53, 77, 513)-Net over F128 — Digital
Digital (24, 77, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
(77−53, 77, 119944)-Net in Base 128 — Upper bound on s
There is no (24, 77, 119945)-net in base 128, because
- 1 times m-reduction [i] would yield (24, 76, 119945)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 14060 783629 918042 068612 563536 602885 356811 220208 397642 898936 052326 695830 998812 192760 354886 838752 356826 190405 711784 130323 124425 482950 856789 585333 929052 589628 437312 > 12876 [i]