Best Known (10, 10+32, s)-Nets in Base 128
(10, 10+32, 288)-Net over F128 — Constructive and digital
Digital (10, 42, 288)-net over F128, using
- t-expansion [i] based on digital (9, 42, 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
(10, 10+32, 296)-Net over F128 — Digital
Digital (10, 42, 296)-net over F128, using
- net from sequence [i] based on digital (10, 295)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 10 and N(F) ≥ 296, using
(10, 10+32, 321)-Net in Base 128
(10, 42, 321)-net in base 128, using
- 22 times m-reduction [i] based on (10, 64, 321)-net in base 128, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
(10, 10+32, 18196)-Net in Base 128 — Upper bound on s
There is no (10, 42, 18197)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 31852 818768 769865 399070 687472 215887 531276 471588 764387 893431 494978 546326 871153 618579 680765 > 12842 [i]