MinT - Best Known (222−99, 222, s)-Nets in Base 4

Best Known (222−99, 222, s)-Nets in Base 4

(222−99, 222, 130)-Net over F₄ — Constructive and digital

Digital (123, 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]

(222−99, 222, 226)-Net over F₄ — Digital

Digital (123, 222, 226)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−99, 222, 3268)-Net in Base 4 — Upper bound on s

There is no (123, 222, 3269)-net in base 4, because

1 times m-reduction [i] would yield (123, 221, 3269)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 505876 067508 018811 023736 799463 813842 661023 357988 981573 084338 815104 283683 330061 489197 753855 139222 151066 152460 937418 286066 586570 293504 > 4²²¹ [i]