Best Known (64, 64+143, s)-Nets in Base 4
(64, 64+143, 66)-Net over F4 — Constructive and digital
Digital (64, 207, 66)-net over F4, using
- t-expansion [i] based on digital (49, 207, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(64, 64+143, 99)-Net over F4 — Digital
Digital (64, 207, 99)-net over F4, using
- t-expansion [i] based on digital (61, 207, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(64, 64+143, 451)-Net in Base 4 — Upper bound on s
There is no (64, 207, 452)-net in base 4, because
- 1 times m-reduction [i] would yield (64, 206, 452)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11915 362977 449536 710577 257269 392172 601746 829239 617015 598886 980523 409579 409365 089078 550699 416413 667308 051097 357433 601819 820640 > 4206 [i]