Best Known (128, 128+100, s)-Nets in Base 4
(128, 128+100, 130)-Net over F4 — Constructive and digital
Digital (128, 228, 130)-net over F4, using
- t-expansion [i] based on digital (105, 228, 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
(128, 128+100, 244)-Net over F4 — Digital
Digital (128, 228, 244)-net over F4, using
(128, 128+100, 3572)-Net in Base 4 — Upper bound on s
There is no (128, 228, 3573)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 187208 260332 581884 074425 109064 594669 950932 008198 618970 482981 983182 406976 494514 653275 318270 346877 212180 500170 575954 284976 117250 795116 150178 > 4228 [i]