Best Known (6, 6+54, s)-Nets in Base 128
(6, 6+54, 216)-Net over F128 — Constructive and digital
Digital (6, 60, 216)-net over F128, using
- t-expansion [i] based on digital (5, 60, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(6, 6+54, 243)-Net over F128 — Digital
Digital (6, 60, 243)-net over F128, using
- net from sequence [i] based on digital (6, 242)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 6 and N(F) ≥ 243, using
(6, 6+54, 4129)-Net in Base 128 — Upper bound on s
There is no (6, 60, 4130)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 2 715188 325039 337156 221100 665065 398616 769504 865613 317942 555407 470396 470240 916627 013372 415300 213505 040508 550679 697734 809334 079888 > 12860 [i]