Best Known (10, 10+34, s)-Nets in Base 128
(10, 10+34, 288)-Net over F128 — Constructive and digital
Digital (10, 44, 288)-net over F128, using
- t-expansion [i] based on digital (9, 44, 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+34, 296)-Net over F128 — Digital
Digital (10, 44, 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+34, 321)-Net in Base 128
(10, 44, 321)-net in base 128, using
- 20 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+34, 16064)-Net in Base 128 — Upper bound on s
There is no (10, 44, 16065)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 521 559564 260012 727557 869098 543159 209384 284854 493518 542287 270012 525514 532325 718031 272000 174656 > 12844 [i]