MinT - Best Known (222−116, 222, s)-Nets in Base 4

Best Known (222−116, 222, s)-Nets in Base 4

(222−116, 222, 130)-Net over F₄ — Constructive and digital

Digital (106, 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]

(222−116, 222, 144)-Net over F₄ — Digital

Digital (106, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(222−116, 222, 1461)-Net in Base 4 — Upper bound on s

There is no (106, 222, 1462)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 798772 800332 054196 652714 133838 480489 789537 260615 265087 970267 569748 646056 840247 511530 490761 530185 771080 907072 289329 662090 413938 159840 > 4²²² [i]