Best Known (6, 6+47, s)-Nets in Base 128
(6, 6+47, 216)-Net over F128 — Constructive and digital
Digital (6, 53, 216)-net over F128, using
- t-expansion [i] based on digital (5, 53, 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+47, 243)-Net over F128 — Digital
Digital (6, 53, 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+47, 4301)-Net in Base 128 — Upper bound on s
There is no (6, 53, 4302)-net in base 128, because
- 1 times m-reduction [i] would yield (6, 52, 4302)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 37 611895 495255 238499 941542 330096 536894 517862 774277 682936 938603 091032 325217 918015 861938 357579 489192 474567 659376 > 12852 [i]