Best Known (72−61, 72, s)-Nets in Base 128
(72−61, 72, 288)-Net over F128 — Constructive and digital
Digital (11, 72, 288)-net over F128, using
- t-expansion [i] based on digital (9, 72, 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
(72−61, 72, 296)-Net over F128 — Digital
Digital (11, 72, 296)-net over F128, using
- t-expansion [i] based on digital (10, 72, 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
- net from sequence [i] based on digital (10, 295)-sequence over F128, using
(72−61, 72, 321)-Net in Base 128
(11, 72, 321)-net in base 128, using
- base change [i] based on digital (2, 63, 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
(72−61, 72, 9190)-Net in Base 128 — Upper bound on s
There is no (11, 72, 9191)-net in base 128, because
- 1 times m-reduction [i] would yield (11, 71, 9191)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 409450 174815 681207 195877 055575 597130 391267 047231 188143 005776 765287 043994 516562 071551 157892 995952 496853 738105 760289 288497 797910 599054 617115 846997 827628 > 12871 [i]