Best Known (10, 10+68, s)-Nets in Base 128
(10, 10+68, 288)-Net over F128 — Constructive and digital
Digital (10, 78, 288)-net over F128, using
- t-expansion [i] based on digital (9, 78, 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+68, 296)-Net over F128 — Digital
Digital (10, 78, 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+68, 7258)-Net in Base 128 — Upper bound on s
There is no (10, 78, 7259)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 230 689225 640632 654281 928949 453757 127097 653216 472997 538585 333213 290809 996304 066307 627218 982702 920634 433440 793065 314241 485948 007301 888340 002653 439355 590564 397597 967170 > 12878 [i]