MinT - Best Known (212−93, 212, s)-Nets in Base 4

Best Known (212−93, 212, s)-Nets in Base 4

(212−93, 212, 130)-Net over F₄ — Constructive and digital

Digital (119, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 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]

(212−93, 212, 228)-Net over F₄ — Digital

Digital (119, 212, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−93, 212, 3427)-Net in Base 4 — Upper bound on s

There is no (119, 212, 3428)-net in base 4, because

1 times m-reduction [i] would yield (119, 211, 3428)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 895689 466682 351578 602855 544483 965413 813400 676577 433242 131880 031780 037802 931623 344212 922669 156744 391305 493394 902230 333844 050800 > 4²¹¹ [i]