MinT - Best Known (222−110, 222, s)-Nets in Base 4

Best Known (222−110, 222, s)-Nets in Base 4

(222−110, 222, 130)-Net over F₄ — Constructive and digital

Digital (112, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(222−110, 222, 165)-Net over F₄ — Digital

Digital (112, 222, 165)-net over F₄, using

t-expansion [i] based on digital (109, 222, 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]

(222−110, 222, 1870)-Net in Base 4 — Upper bound on s

There is no (112, 222, 1871)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 649472 846912 462282 991077 928682 390584 421688 226280 529194 435213 096333 986879 523311 833871 471857 641681 293096 776364 807556 494402 716267 337456 > 4²²² [i]