MinT - Best Known (222−104, 222, s)-Nets in Base 4

Best Known (222−104, 222, s)-Nets in Base 4

(222−104, 222, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(222−104, 222, 194)-Net over F₄ — Digital

Digital (118, 222, 194)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−104, 222, 2464)-Net in Base 4 — Upper bound on s

There is no (118, 222, 2465)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 205086 387397 674190 071787 568444 554828 448485 847987 944407 414688 402379 182565 898869 719239 029084 604843 461087 055132 153042 063806 354356 253280 > 4²²² [i]