Best Known (67, 67+97, s)-Nets in Base 4
(67, 67+97, 66)-Net over F4 — Constructive and digital
Digital (67, 164, 66)-net over F4, using
- t-expansion [i] based on digital (49, 164, 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
(67, 67+97, 99)-Net over F4 — Digital
Digital (67, 164, 99)-net over F4, using
- t-expansion [i] based on digital (61, 164, 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
(67, 67+97, 653)-Net in Base 4 — Upper bound on s
There is no (67, 164, 654)-net in base 4, because
- 1 times m-reduction [i] would yield (67, 163, 654)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 142 222234 304524 830029 772364 238872 542651 141295 721167 304000 191861 744806 496220 549451 698536 687889 574904 > 4163 [i]