Best Known (133, 133+108, s)-Nets in Base 4
(133, 133+108, 130)-Net over F4 — Constructive and digital
Digital (133, 241, 130)-net over F4, using
- t-expansion [i] based on digital (105, 241, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(133, 133+108, 239)-Net over F4 — Digital
Digital (133, 241, 239)-net over F4, using
(133, 133+108, 3355)-Net in Base 4 — Upper bound on s
There is no (133, 241, 3356)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12 676935 202160 677473 193288 629558 433547 549679 796613 249578 445172 131072 072201 457225 300692 386696 644211 233580 312244 020963 875430 039410 105864 273076 095376 > 4241 [i]