MinT - Best Known (110, 110+106, s)-Nets in Base 4

Best Known (110, 110+106, s)-Nets in Base 4

(110, 110+106, 130)-Net over F₄ — Constructive and digital

Digital (110, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(110, 110+106, 165)-Net over F₄ — Digital

Digital (110, 216, 165)-net over F₄, using

t-expansion [i] based on digital (109, 216, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(110, 110+106, 1908)-Net in Base 4 — Upper bound on s

There is no (110, 216, 1909)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11361 613744 237008 651166 260840 262368 346576 391249 287480 527672 476930 778207 780706 000975 193318 346538 663159 131282 708433 563570 505687 785340 > 4²¹⁶ [i]