Best Known (106, 106+80, s)-Nets in Base 4
(106, 106+80, 130)-Net over F4 — Constructive and digital
Digital (106, 186, 130)-net over F4, using
- t-expansion [i] based on digital (105, 186, 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
(106, 106+80, 217)-Net over F4 — Digital
Digital (106, 186, 217)-net over F4, using
(106, 106+80, 3280)-Net in Base 4 — Upper bound on s
There is no (106, 186, 3281)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9677 902408 065114 857845 990050 023261 647312 426056 259231 614187 856364 141494 891677 075435 794889 254424 817351 067441 653596 > 4186 [i]