Best Known (69−59, 69, s)-Nets in Base 128
(69−59, 69, 288)-Net over F128 — Constructive and digital
Digital (10, 69, 288)-net over F128, using
- t-expansion [i] based on digital (9, 69, 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
(69−59, 69, 296)-Net over F128 — Digital
Digital (10, 69, 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
(69−59, 69, 8009)-Net in Base 128 — Upper bound on s
There is no (10, 69, 8010)-net in base 128, because
- 1 times m-reduction [i] would yield (10, 68, 8010)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 195639 570950 816394 445988 120197 620494 988287 415841 202947 473974 772642 585688 623232 365169 427671 246880 894776 962554 616963 375699 133136 393455 784438 942608 > 12868 [i]