Best Known (64−54, 64, s)-Nets in Base 128
(64−54, 64, 288)-Net over F128 — Constructive and digital
Digital (10, 64, 288)-net over F128, using
- t-expansion [i] based on digital (9, 64, 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
(64−54, 64, 296)-Net over F128 — Digital
Digital (10, 64, 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
(64−54, 64, 321)-Net in Base 128
(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
(64−54, 64, 8487)-Net in Base 128 — Upper bound on s
There is no (10, 64, 8488)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 727 270521 953064 374639 277550 961888 972712 616112 053335 531510 985699 669411 460679 213305 648219 737873 207213 752747 205869 716854 521088 758618 619492 > 12864 [i]