MinT - Best Known (127, 127+111, s)-Nets in Base 4

Best Known (127, 127+111, s)-Nets in Base 4

(127, 127+111, 130)-Net over F₄ — Constructive and digital

Digital (127, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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+111, 209)-Net over F₄ — Digital

Digital (127, 238, 209)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+111, 2749)-Net in Base 4 — Upper bound on s

There is no (127, 238, 2750)-net in base 4, because

1 times m-reduction [i] would yield (127, 237, 2750)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48916 383152 742247 670552 310967 045610 764058 467555 683016 556899 323656 360425 225808 676966 229072 308636 343813 043943 603818 226637 551627 261690 293536 582756 > 4²³⁷ [i]