Best Known (117, 117+80, s)-Nets in Base 4
(117, 117+80, 130)-Net over F4 — Constructive and digital
Digital (117, 197, 130)-net over F4, using
- t-expansion [i] based on digital (105, 197, 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
(117, 117+80, 275)-Net over F4 — Digital
Digital (117, 197, 275)-net over F4, using
(117, 117+80, 4818)-Net in Base 4 — Upper bound on s
There is no (117, 197, 4819)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 40657 079728 366755 459940 740203 965639 312924 390730 343835 224539 232534 214155 839570 954604 619579 950251 474838 455429 581467 524620 > 4197 [i]