MinT - Best Known (127, 127+125, s)-Nets in Base 4

Best Known (127, 127+125, s)-Nets in Base 4

(127, 127+125, 130)-Net over F₄ — Constructive and digital

Digital (127, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(127, 127+125, 181)-Net over F₄ — Digital

Digital (127, 252, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+125, 2133)-Net in Base 4 — Upper bound on s

There is no (127, 252, 2134)-net in base 4, because

1 times m-reduction [i] would yield (127, 251, 2134)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 368764 825951 466419 089628 075618 564568 151123 428142 146986 682369 034547 227133 705676 040214 920428 365269 819918 239993 921165 344495 847976 478975 744543 054893 676320 > 4²⁵¹ [i]